I'm not sure if this exact situation is addressed in Canon Law but I believe what is addresses and requires is that the Godparents be baptized Catholics who are in good standing with the Church. This is also true of the parents wherein the child that is being baptized is being done so on the faith and promise of the parents to raise the child in the faith and not alcafeteria style either; though sadly this isn't always the case.
I'm sure the child's father can speak with the parish's father and make his objections known. Maybe there's recourse there.
Baptizing isn't a joke thing. It's the initiation rite into the Christian faith. This is the Sacrament that opens all others because you are cleansed of all sin up to that point and born anew. This is not a symbolic gesture but an act of faith that leaves an indelible mark on your soul. The baptized is now set apart.