1. The Eucharist is NOT to be consumed except by Catholics who have been previously washed clean of Mortal Sin through Confession.

St. Justin the Martyr, Father of the Church writes Chapter 66 of his First Apology. "This food is called among us Ε?χαριστ?α [the Eucharist], of which no one is allowed to partake but the man who believes that the things which we teach are true, and who has been washed with the washing that is for the remission of sins, and unto regeneration, and who is so living as Christ has enjoined. For not as common bread and common drink do we receive these; but in like manner as Jesus Christ our Saviour, having been made flesh by the Word of God, had both flesh and blood for our salvation, so likewise have we been taught that the food which is blessed by the prayer of His word, and from which our blood and flesh by transmutation are nourished, is the flesh and blood of that Jesus who was made flesh."

The current Code of Canon Law repeats, "A person who is conscious of grave sin is not to celebrate Mass or receive the body of the Lord without previous sacramental confession unless there is a grave reason and there is no opportunity to confess; in this case the person is to remember the obligation to make an act of perfect contrition which includes the resolution of confessing as soon as possible." (Can. 916)

Another very important one is Canon 915, which Bishops today would do well to remember, "Can. 915 Those who have been excommunicated or interdicted after the imposition or declaration of the penalty and others obstinately persevering in manifest grave sin are not to be admitted to holy communion."

2. Abortion supersedes "social justice" issues in its moral gravity.

"The inviolability of the person which is a reflection of the absolute inviolability of God, fínds its primary and fundamental expression in the inviolability of human life. Above all, the common outcry, which is justly made on behalf of human rights-for example, the right to health, to home, to work, to family, to culture- is false and illusory if the right to life, the most basic and fundamental right and the condition for all other personal rights, is not defended with maximum determination." Pope JPII "Christifideles Laici," 

"An extreme sensitivity akin to a holy reaction is felt when attempts on life are made in the form of famine, war, and terrorism; yet, one cannot find this feeling of sensitivity when faced with abortion, which takes the lives of innumerable innocent beings." John Paul II February 12, 1986

St. John Chrysostom calls abortion "something worse than murder", "Homily 24 on Romans,"

" In our nation, abortion and euthanasia have become preeminent threats to human dignity because they directly attack life itself, the most fundamental human good and the condition for all others”  USCCB "Forming Consciences for Faithful Citizenship, no. 22

3. All forms of contraception, masturbation, sterilization and the like are gravely sinful.

Catechism of the Catholic Church #2351-2359:

"Offenses against chastity

2351 Lust is disordered desire for or inordinate enjoyment of sexual pleasure. Sexual pleasure is morally disordered when sought for itself, isolated from its procreative and unitive purposes.

2352 By masturbation is to be understood the deliberate stimulation of the genital organs in order to derive sexual pleasure. "Both the Magisterium of the Church, in the course of a constant tradition, and the moral sense of the faithful have been in no doubt and have firmly maintained that masturbation is an intrinsically and gravely disordered action."138 "The deliberate use of the sexual faculty, for whatever reason, outside of marriage is essentially contrary to its purpose." For here sexual pleasure is sought outside of "the sexual relationship which is demanded by the moral order and in which the total meaning of mutual self-giving and human procreation in the context of true love is achieved."139

To form an equitable judgment about the subjects' moral responsibility and to guide pastoral action, one must take into account the affective immaturity, force of acquired habit, conditions of anxiety or other psychological or social factors that lessen, if not even reduce to a minimum, moral culpability.

2353 Fornication is carnal union between an unmarried man and an unmarried woman. It is gravely contrary to the dignity of persons and of human sexuality which is naturally ordered to the good of spouses and the generation and education of children. Moreover, it is a grave scandal when there is corruption of the young.

2354 Pornography consists in removing real or simulated sexual acts from the intimacy of the partners, in order to display them deliberately to third parties. It offends against chastity because it perverts the conjugal act, the intimate giving of spouses to each other. It does grave injury to the dignity of its participants (actors, vendors, the public), since each one becomes an object of base pleasure and illicit profit for others. It immerses all who are involved in the illusion of a fantasy world. It is a grave offense. Civil authorities should prevent the production and distribution of pornographic materials.

2355 Prostitution does injury to the dignity of the person who engages in it, reducing the person to an instrument of sexual pleasure. The one who pays sins gravely against himself: he violates the chastity to which his Baptism pledged him and defiles his body, the temple of the Holy Spirit.140 Prostitution is a social scourge. It usually involves women, but also men, children, and adolescents (The latter two cases involve the added sin of scandal.). While it is always gravely sinful to engage in prostitution, the imputability of the offense can be attenuated by destitution, blackmail, or social pressure.

2356 Rape is the forcible violation of the sexual intimacy of another person. It does injury to justice and charity. Rape deeply wounds the respect, freedom, and physical and moral integrity to which every person has a right. It causes grave damage that can mark the victim for life. It is always an intrinsically evil act. Graver still is the rape of children committed by parents (incest) or those responsible for the education of the children entrusted to them.

Chastity and homosexuality

2357 Homosexuality refers to relations between men or between women who experience an exclusive or predominant sexual attraction toward persons of the same sex. It has taken a great variety of forms through the centuries and in different cultures. Its psychological genesis remains largely unexplained. Basing itself on Sacred Scripture, which presents homosexual acts as acts of grave depravity,141 tradition has always declared that "homosexual acts are intrinsically disordered."142 They are contrary to the natural law. They close the sexual act to the gift of life. They do not proceed from a genuine affective and sexual complementarity. Under no circumstances can they be approved.

2358 The number of men and women who have deep-seated homosexual tendencies is not negligible. This inclination, which is objectively disordered, constitutes for most of them a trial. They must be accepted with respect, compassion, and sensitivity. Every sign of unjust discrimination in their regard should be avoided. These persons are called to fulfill God's will in their lives and, if they are Christians, to unite to the sacrifice of the Lord's Cross the difficulties they may encounter from their condition.

2359 Homosexual persons are called to chastity. By the virtues of self-mastery that teach them inner freedom, at times by the support of disinterested friendship, by prayer and sacramental grace, they can and should gradually and resolutely approach Christian perfection."

See also Persona Humana from the Congregation of the Doctrine of the Faith, Pope Paul VI "Humanae Vitae," Pope Pius XII, "Allocutio" Oct 8th, 1953, and Summa Theologica IIª-IIae, q. 154 a. 11. St. August., De nupt. et concupisc., cap. XV.

4. IVF (in vitro fertilization) or any other use of artificial fertilization, is gravely immoral. 

"the manner in which human conception is achieved with IVF and ET cannot be approved," CDF, Donum vitae II, 1.,

"This moral condemnation also regards procedures that exploit living human embryos and fetuses-sometimes specifically "produced" for this purpose by in vitro fertilization-either to be used as "biological material" or as providers of organs or tissue for transplants in the treatment of certain diseases. The killing of innocent human creatures, even if carried out to help others, constitutes an absolutely unacceptable act." Pope JPII "Evangelium Vitae"

"2376 Techniques that entail the dissociation of husband and wife, by the intrusion of a person other than the couple (donation of sperm or ovum, surrogate uterus), are gravely immoral. These techniques (heterologous artificial insemination and fertilization) infringe the child's right to be born of a father and mother known to him and bound to each other by marriage. They betray the spouses' "right to become a father and a mother only through each other." Catechism of the Catholic Church #2376

see also Pope Benedict XVI Address Feb 27 2006, 

5. The Faithful are NOT To Use the "Orans" Posture During the Our Father.

See this excellent, concise article here. The author specifically uses an official Vatican Document from 1997 to back up his claims. Well worth the read!

6. The Belief in the "Evolution of Doctrine" is a Heresy.

Pope Gregory XVI wrote two encyclicals concerning the work of Catholic priest Father Hugues-Félicité Robert de Lamennais. The second encyclical, "Singulari nos" officially proclaimed Lamennais excommunicated from the Church, while the first, "Mirari vos," condemned his works and beliefs. In, "Singulari Nos," the Pope clearly condemns the idea (among others) that Lamennais promoted that "The elevation of reason and individualism over faith and tradition: Lamennais believed that reason and individual experience were the ultimate sources of truth and that the Church should adapt its teachings to modern conditions, which is a core tenet of the heresy of modernism."

Later, Pope St. Pius X condemned the heresy of Modernism in his encyclical "Lamentabili Sane," writing that it is a gross error to believe that, "59. Christ did not teach a determined body of doctrine applicable to all times and all men, but rather inaugurated a religious movement adapted or to be adapted to different times and places. 

62. The chief articles of the Apostles’ Creed did not have the same sense for the Christians of the first ages as they have for the Christians of our time.

63. The Church shows that she is incapable of effectively maintaining evangelical ethics since she obstinately clings to immutable doctrines which cannot be reconciled with modern progress.

64. Scientific progress demands that the concepts of Christian doctrine concerning God, creation, revelation, the Person of the Incarnate Word, and Redemption be re-adjusted."

The Pope clearly "condemned and proscribed" these and many other errors in this official document. 

7. The Belief that Separation of Church and State is a good thing is an Error.

In the Syllabus of Errors, Pope Blessed Pius IX proclaims that it is an ERROR to believe that "55. The Church ought to be separated from the .State, and the State from the Church." 

This website clearly explains that Separation of Church and State was rejected by numerous Sovereign Pontiffs, notably such as:

Gregory XVI:  Encyclical: Mirari vos, Aug. 15, 1832. (PE 33; 20)

Pius IX:  Allocution to the Consistory: Acerbissimum, Sept. 27, 1852.
Encyclical: Quanta cura, Dec. 8, 1864. (PE 63)
Syllabus, Dec. 8, 1864: prop 55.

Leo XIII: Encyclical: Cum multa, Dec. 8, 1882. (PE 88)
Encyclical: Humanum genus, April 20, 1884. (PE 91; 13 ff)
Encyclical: Immortale Dei, Nov. 1, 1885. (PE 93; 27 ff)
Encyclical: Libertas, June 20, 1888. (PE 103; 18 ff)
Encyclical: Au milieu des sollicitudes, Feb. 16, 1892. (PE 119; 28 ff)
Letter Longinqua, Jan. 6, 1895. (PE 134; 3 ff)

Saint Pius X:  Allocution to the Secret Consistory, Amplissimum coetum, March 27, 1905.
Encyclical: Vehementer Nos, Feb. 11, 1906. (PE 169; 1 ff)
Allocution to the Consistory: Gravissimum apostolici, Feb. 21, 1906.
Encyclical: Gravissimo officii, Aug. 10, 1906. (PE 172; 1 ff)
Letter: Le moment, May 17, 1908.
Encyclical: Jamdudum, May 24, 1911. (PE 177; 2 ff)

Pius XI:  Encyclical Maximam Gravissimamque, Jan. 18, 1924. (PE 196; 2 ff)
Allocution: Jam annus, to the Secret Consistory, Dec. 14, 1925.
Encyclical: Iniquis afflictisque, Nov. 18, 1926. (PE 200; 8 ff)
Encyclical: Dilectissima Nobis, June 3, 1933. (PE 215; 6 ff)

Pius XII:  Allocution to some Italian Catholic Jurists, Dec. 6, 1953.

Why is the saying that the State and the Church must necessarily be separated a false and dangerous theory?
There is a pernicious error in saying Church and State necessarily must function separately:

First reason: "Based, as it is, on the principle that the State must not recognise any religious cult, it is in the first place guilty of a great injustice to God; for the Creator of man is also the Founder of human societies, and preserves their existence as He preserves our own.  We owe Him, therefore, not only a private cult, but a public and social worship to honour Him."

Second reason: "This thesis is an obvious negation of the supernatural order.  It limits the action of the State to the pursuit of public prosperity during this life only, which is but the proximate object of political societies; and it occupies itself in no fashion (on the plea that this is foreign to it) with their ultimate object which is man's eternal happiness after this short life shall have run its course.  But as the present order of things is temporary and subordinated to the achievement of man's supreme and absolute welfare, it follows that the civil power must not only place no obstacle in the way of this achievement, but must aid us in effecting it."

Third reason: "The same thesis (...) upsets the order providentially established by God in the world, which demands a harmonious agreement between the two societies.  Both of them, the civil and the religious society, have in fact the same subjects, although each exercises in its own sphere its authority over them.  It follows necessarily that there are many things belonging to them in common in which both societies must have relations with one another.  Remove the agreement between Church and State, and the result will be that from these converging interests will spring the seeds of disputes which will become very conflicting on both sides; it will become more difficult to see where the truth lies, and great confusion is certain to arise."

Fourth reason: "This thesis inflicts great injury on society itself, for it cannot either prosper or last long when due place is not left for religion, which is the supreme rule and the sovereign mistress in all questions touching the rights and duties of men."  [Pius X: Encyclical: Vehementer nos, Feb. 11, 1906. (PE 169; 3)]

How can it be claimed that the separation of Church and State is absurd?
"As soon as the State refuses to give to God what belongs to God, by a necessary consequence it refuses to give to citizens that to which, as men, they have a right; as, whether agreeable or not to accept, it cannot be denied that man's rights spring from his duty toward God.  Whence it follows that the State, by missing in this connection the principal object of its institution, finally becomes false to itself by denying that which is the reason of its own existence.  These superior truths are so clearly proclaimed by the voice of even natural reason, that they force themselves upon all who are not blinded by the violence of passion."  [Leo XIII, Encyclical: Au milieu des sollicitudes, Feb. 16, 1892. (PE 119; 28)]"

In Conclusion

Yes, it is scary how little we know our Faith today, which is why it is vitally important that we learn our Faith well now when we can. It matters little our level of discomfort or distaste towards any one of these aforementioned teachings of the Church. What matters is that we, as baptized members of the Catholic Church, ACCEPT THEM!