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in the Presbyterian/United Church of Christ traditions, I would not officiate at a baptism where the parents "contacted" my church, but had no connection with it. A Baptism is part of a regular church service where parents do indeed promise to raise their child in the Christian faith, and the congregation promises to be part of the child's nurturing. However,it is also a pastoral reality that someone whose parents are faithful members of my congregation, or someone who comes in sporadically, and declares every intention of being faithful, will request baptism, and in those cases I would say yes, and not be too shocked if those promises are unfulfilled.
In Reformed Tradition churches, baptism is not required to save a person's soul. It marks us as part of the Christian community, and acknowledges both the relationship that God has with a person, and in the case of parents having children baptised, recognizes their including those children in the covenant community (which, as someone stated, is self-affirmed in a young person's confirmation).
The parents' marital status would have no bearing on my willingness to do a baptism, though if parents were _planning_ on getting married, I might discuss the order of these ceremonies.