Simplistic Paraphrasing of the Summa Theologica
The question seems to be about Baptism, but it is really about two other Protestant doctrines.
1. The perspicuity of Scripture. Perspicuity means, “crystal clearl and therefore, easy to understand”.
2. And Scripture as the sole rule of faith (i.e. the Bible alone).
Perspicuity of Scripture
Now, if it were true that Scripture was crystal clear and easy to understand, then they would be able to agree upon the nature of Baptism. But, in fact, Scripture is so unclear about the nature of Baptism, that Protestants have come up with several contradicting teachings on Baptism. And they base all of these teachings upon their own personal twist of the Bible alone.
Therefore, Lutherans believe in Baptismal Regeneration. They believe the Bible teaches that Baptism regenerates the soul. In what way, is unclear, since they simultaneously believe that justification is only forensic. In other words, that they are only covered over with the righteousness of Christ, but otherwise, remain sinners.
Presbyterians believe in Covenantal Baptism. They believe that Baptism is a sign a covenant with God and seal of righteousness, the way that circumcision was in the Old Testament. In what way it is a sign, is unclear. Since they also believe in forensic justification and therefore, that there is no change in the soul.
The Churches of Christ proclaim Salvation Occasion Baptism. Although they have no agreed upon doctrines that they must hold, someone came up with the idea that it is in Baptism that one is saved. They have merely replaced the “altar call” of other Protestant confessions, with water Baptism.
Baptists hold to a Believer’s Baptism. This is the belief that one is saved by a profession of faith. And then the Baptism is simply done in obedience to Christ.
And of course, there are many Protestants who don’t believe that water Baptism is, at all, necessary.
Sole rule of faith
It is obvious, above, that Protestants only give lip service to the idea of the Scriptures as the sole rule of faith. After all, Lutherans believe Lutherans. Presbyterians believe Presbyterians. The Churches of Christ pretty much decide for themselves, individually. And Baptists, believe Baptists. The Bible doesn't teach four baptisms.
They claim that they are all following the Bible alone. But the Bible alone is leading to inconclusive and contradictory results. The situation on Baptism is not isolated. They have five views on the Eucharist, four on salvation, five on sanctification, etc. etc.
Ask yourself, "does the Bible alone teach confusion?" If reading the Bible alone leads to inconclusive and contradictory results, the results speak for themselves.
What about Catholics?
We continue to believe what Jesus Christ taught. The Catholic Church passes on these beliefs by Sacred Tradition and Scripture. It is the Catholic Church which wrote about Baptism, in the Bible. Let me repeat, it is the Catholic Church’s writings which Protestants are interpreting wrongly, because it is the Catholic Church which wrote about Baptism, in the New Testament.
What does the New Testament say?
The Catholic Church teaches through the Bible. And the Bible says:
Hebrews 13:7 Remember them which have the rule over you, who have spoken unto you the word of God: whose faith follow, considering the end of their conversation.
And here’s what our Rulers in the Church teach about Baptism:
CCC#1213 Holy Baptism is the basis of the whole Christian life, the gateway to life in the Spirit (vitae spiritualis ianua),4 and the door which gives access to the other sacraments. Through Baptism we are freed from sin and reborn as sons of God; we become members of Christ, are incorporated into the Church and made sharers in her mission: "Baptism is the sacrament of regeneration through water in the word."5
There’s no confusion, here. Because it is through the Catholic Church, that God speaks.