“This is because of the Baptist doctrine of adult baptism.”
I think that is more correctly called BELIEVERS’ baptism. Some of those who are baptised are children who are old enough to understand and accept the Gospel, but could, for instance be aged as low as 7 or 8, ie definitely not adults.
You are correct. A person does not have to be an adult, but only of the age of consent. This is similar to the Catholic sacrament of confirmation, and to the Jewish rite of bar mitzah. By tradition, a boy - considered to be a young adult - bar mitzah’s at age 13, and a girl at age 12 plus 1 day. As for me, I don’t see that Jesus was bar mitzah’d. Rather, he was circumcised on the 8th day and baptized as an adult. Baptism, according to Baptists, is a sacrament of forgiveness envisioned as re-birth. It should seal the deal. At that time, even though you will undoubtedly continue to sin, your sins are forgiven. This is not a license to sin. We sin because we are weak and ignorant, but we commit ourselves to follow Jesus although we know we will not do so perfectly. Baptism at the time of Jesus was a bit different. It, too, signified forgiveness. This would include ritual washing as after a woman’s period or after touching something unclean. These baptisms would be periodic. If anything, Muslims are even more adamant washing. But, the baptism of Jesus portrayed in the bible is a special immersion. In this form of immersion you signify whose interpretation of scripture you will follow. For example. Rabbi Hillel or Rabbi Shammai. This is why John said to Jesus, you should baptize me, as John was merely the herald and Jesus is our great teacher. But Jesus said he needed to be baptized. So, if we follow Jesus, baptism is a sign both of forgiveness and that we follow his interpretation of scripture. According to Maimonides, both circumcision and baptism are good, circumcision representing dedication to the law, and baptism forgiveness. But, of the two, baptism is better.