The Church says, also in canon law, that the baptism of a child must include a guarantee, or at least some assurance that the child will be educated in the faith of the baptism. This is a basic requirement of the Church, and therefore, the Church requires godparents for the baptism of children. But there can be exceptions.
First, we have to distinguish if there is, let us say, a cohabitation of a man and a woman. At least this union is not against nature; it is not a same-sex union. This is a basic and substantial difference compared to a so-called same-sex union. In the case of simple cohabitation, we can more easily give baptism to the children of such a union, of a man and a woman, provided there is a good godfather or godmother. I can seek for them a good person who will pray for the child and teach the child, such as a grandmother, uncle, or so else. We should try to do this to help ensure that the child is freed from original sin and receives the graces of baptism. So here, we have to be wise and ensure that the child is not deprived of these unspeakable graces.
In the other case, a so-called same-sex union, of homosexuals or lesbians, when they come and declare, "We are living together as a same-sex couple," in this case, I think one should not give baptism to their so-called child, because this is against nature. It is a different situation. We would, in some way, be implicitly recognizing the licitness of their union and collaborating with the normalization of these unions. In this case, it is better not to give baptism, but perhaps to find someone who will pray for the child so that, when the child becomes an adult or at least reaches the age of reason, they can decide for themselves and ask for baptism.
We can find a person who will pray for this child, but not proceed with baptism because of the situation involving the same-sex union of those so-called parents. They are usually not true parents.
Another case is when there is a single lesbian woman, let's say, who is not living with anyone. In this case, I think we can proceed, provided there is a good godfather or godmother, someone who will pray for the child. So, we have to distinguish between the situations.
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