The theology may be appalling, but shouldn’t the baby receive the sacraments of his church?
Years ago, in Spain, my little cousin was denied baptism because his parents were not married in the Catholic church (the mom was Lutheran). Since a baptism certificate was then necessary for just about anything in Spain, beginning with registering for kindergarten, the parents agreed to get married again. Then it turned out that no priest would marry them as long as the mother was Lutheran, and she refused to convert just to go along. Eventually a priest married them in the sacristy and a few days later the boy was baptized.
The child should be baptized period. That is what Jesus would do and then He would pray for the child and her parents. People need to concentrate on the sins they themselves are committing and quit judging others. God doesn’t have a “sin hierarchy” and we all sin regularily.
Yes.
The rite of Baptism even includes an exorcism:
V. Do you reject Satan?
R. I do.
V. And all his works?
R. I do.
V. And all his empty promises?
R. I do.
However, if you're dealing with people raising the child who have a public commitment to lesbian sin (a commitment they have shown in the most public way possible: pseudo-marriage), you do not have this sincere intent.
Baptism is not some kind of magic. Sincere intent is always required, otherwise it is fraudulent and, in fact, a sacrilege.
Exactly, the baby has done nothing wrong.