Should children of same sex and unwed families be baptized?

The baptism of the children of a second (civil) marriage where they are Mass goers is also allowed and even encouraged.

Therefore it would seem even the ongoing material sin of the parents is not an apriori obstacle to the children of public sinners being baptised. That suggests the judgement is an aposteriori one.

That is, its a prudential judgement by the legitimate local authority based on circumstances - material "scandal" not withstanding this important gift.