Here's the current practice in the USA:
Baptism of children in the care of same-sex couples presents a serious pastoral
concern. Nevertheless, the Church does not refuse the Sacrament of Baptism to these children, but there must be a well founded hope that the children will be brought up in the Catholic religion. In those cases where Baptism is permitted, pastoral ministers should exercise prudential judgment when preparing baptismal ceremonies. Also, in preparing the baptismal record, a distinction should be made between natural parents and adoptive parents.
cf. Ministry to Persons with a Homosexual Inclination:
Guidelines for Pastoral Care | USCCB.
these circumstances arose not too long ago in my diocese any Bishop Morlino was quoted
“If the gay couple were to come forward and present the child for baptism and somehow sincerely intend that the child be brought up Catholic, and if an arrangement could be made such that the child being brought up a Catholic was a reasonable hope, then we would strongly favor the baptism of the child,” he said.
If the same-sex couple could not provide that reasonable hope themselves, “then we would try to direct them to choose godparents who could intervene and bring the child up Catholic.”
“We’re not looking for a reason to exclude the child from baptism. We’re looking to create the conditions so that the child can validly and licitly be baptized,” he said.
“That is pastoral service.”
cf. New Pastoral Frontier: Baptisms of Children to Same-Sex Couples | NCR.
Here are some of they ways the synod identified that folks in "Irregular Situations" can get help:
Still another reality on all continents is the existence and activity of Catholic schools and Catholic colleges, in which the children of parents in irregular situations can enroll without any distinction being made.
Instrumentum Laboris - 145
Many times the children are the ones who evangelize their parents.
new initiatives are being enacted, including opportunities for formation in prayer and retreats, intended for parents and often taking place simultaneously with their children’s catechesis in preparation for the sacraments; “schools for parents”; catechetical programs on sexual morality and moral issues related to the family;
ibid. - 147
and it is important to remember that:
Particular Churches are well aware that children or young people are not to blame for the choices and living situation of their parents. Consequently, children are welcome everywhere, without distinction with respect to others and with the same love and attention.
ibid. - 149
but this might be the optimal solution:
In other cases, children of families with irregular situations receive Baptism after three or four years of catechesis, at an age when their peers are admitted to First Communion, as mentioned by some episcopal conferences in Africa.
Like most traditional minded Catholics, I can't see how parents committed to their Irregular Situation (which is my new favorite euphemism) can profess what they need to profess at their children's baptism. (something about rejecting "all Satan's works"). Not that you can stack a remarried Irregular Situation somewhere higher than a same sex Irregular Situation and twice as high as a single parent Irregular Situation, but, there is a certain extra amount of scandal that comes in to the church when considering two fellows telling the congregation a bald-faced lie vs a remarried couple telling a lie one death apart from normalization and a single mother not even remotely telling a lie, but actually needing support from the church community that she's probably not getting.
The only reason I write that is because as you may know, there are only four kinds of ordinary Baptism. (this isn't doctrine, it's just reality). You can be Baptized before Mass, during Mass, after Mass or not at Mass. If I were going to do something that was potentially scandalous, but somehow valid, then I would opt for doing with with the congregation not present.
But, I found this note:
Finally, to prevent the scandal of the weak we are sometimes obliged to sacrifice some temporal good of less importance, but we are not bound to do this when the goods are of greater importance.
interesting when looking up the meaning of the word scandal in the old Catholic Encyclopedia. I'd say Baptism is a good of greater importance (and not a temporal one). So it can't be forsaken to prevent scandal.
And lastly, apply what the Synod folks are saying about the feelings of divorced and remarried Catholics who are unable to receive the Sacraments. One of their major gripes is that it seems like a public punishment. That's not what the sacraments are for, they're medicine if anything. Medicine that can kill you (through Blasphemy) if you receive them unworthily. So perhaps that's why the Synod is finding that they only real confounding factor in allowing children from same sex unions to be baptized is ensuring that they get proper formation in the Faith (and morals) but should not go against what their parents teach because that (undermining the rights of parents to form the their children) is also not what the Church is for as it is not in harmony whatsoever with the Natural Law.
But now we've circled back around and that's why they're called Irregular Situations.