Protestants do not claim to be infallible.
Here is limbo and the necessity for baptism in the Baltimore Catechism.
baltimore-catechism.com/lesson14.htm
Q. 631. Is Baptism necessary to salvation?
A. Baptism is necessary to salvation, because without it we cannot enter into the kingdom of heaven.
Q. 632. Where will persons go who – such as infants – have not committed actual sin and who, through no fault of theirs, die without baptism?
A. Persons, such as infants, who have not committed actual sin and who, through no fault of theirs, die without baptism, cannot enter heaven; but it is the common belief they will go to some place similar to Limbo, where they will be free from suffering, though deprived of the happiness of heaven.
Did you stop reading there, or did you get your information from someone who purposefully edited out pertinent information?
Q. 644. How many kinds of Baptism are there?
A. There are three kinds of Baptism: 1.Baptism of water, of desire, and of blood.
Q. 645. What is Baptism of water?
A. Baptism of water is that which is given by pouring water on the head of the person to be baptized, and saying at the same time, “I baptize thee in the name of the Father, and of the Son, and of the Holy Ghost.”
Q. 646. In how many ways was the baptism of water given in the first ages of the Church?
A. In the first ages of the Church, baptism of water was given in three ways, namely, by immersion or dipping, by aspersion or sprinkling, and by infusion or pouring. Although any of these methods would be valid, only the method of infusion or pouring is now allowed in the Church.
Q. 647. What are the chief ceremonies used in solemn baptism, and what do they signify?
A. The chief ceremonies used in solemn baptism are:
1.A profession of faith and renouncement of the devil to signify our worthiness;
2.The placing of salt in the mouth to signify the wisdom imparted by faith;
3.The holding of the priest’s stole to signify our reception into the Church;
4.The anointing to signify the strength given by the Sacrament;
5.The giving of the white garment or cloth to signify our sinless state after baptism; and
6.The giving of the lighted candle to signify the light of faith and fire of love that should dwell in our souls.
Q. 648. Should one who, in case of necessity, has been baptized with private baptism, be afterwards brought to the Church to have the ceremonies of solemn baptism completed?
A. One who, in case of necessity, has been baptized with private baptism should afterwards be brought to the Church to have the ceremonies of solemn baptism completed, because these ceremonies are commanded by the Church and bring down blessings upon us.
Q. 649. Is solemn baptism given with any special kind of water?
A. Solemn baptism is given with consecrated water; that is, water mixed with holy oil and blessed for baptism on Holy Saturday and on the Saturday before Pentecost. It is always kept in the baptismal font in the baptistry – a place near the door of the Church set apart for baptism.
Q. 650. What is Baptism of desire?
A. Baptism of desire is an ardent wish to receive Baptism, and to do all that God has ordained for our salvation.
Q. 651. What is Baptism of blood?
A. Baptism of blood is the shedding of one’s blood for the faith of Christ.
Q. 652. What is the baptism of blood most commonly called?
A. The baptism of blood is most commonly called martyrdom, and those who receive it are called martyrs. It is the death one patiently suffers from the enemies of our religion, rather than give up Catholic faith or virtue. We must not seek martyrdom, though we must endure it when it comes.
Q. 653. Is Baptism of desire or of blood sufficient to produce the effects of Baptism of water?
A. Baptism of desire or of blood is sufficient to produce the effects of the Baptism of water, if it is impossible to receive the Baptism of water.
Q. 654. How do we know that the baptism of desire or of blood will save us when it is impossible to receive the baptism of water?
A. We know that baptism of desire or of blood will save us when it is impossible to receive the baptism of water, from Holy Scripture, which teaches that love of God and perfect contrition can secure the remission of sins ; and also that Our Lord promises salvation to those who lay down their life for His sake or for His teaching.
Remember, this was intended for young school-age children, as a very basic foundation, and doesn’t treat the matters in any sort of depth whatsoever.
Depending on this for your theology is akin to taking a “Children’s Bible” and trying to prove a theological point from it. It may be a fine vehicle to introduce children, but don’t expect to have a serious discussion based on that alone.