I'm a godfather to some random number of kids, and it's fair to say that for each of the parents I was the least religious person they knew.
What we might call "modern" godparenting is a sort of stand by role if something really bad happens. That means if any of my GCs parents die or become incapacitated I take charge of sorting things out, includuing taking them in if that is appropriate.
It means giving objective advice, and occasionally unthanked role as intermediary in disputes.
As for it being an issue in the eyes of the church, I understand that in general you are supposed to at least be some sort of baptised christian. As it happens I was baptised catholic, but no one has ever asked, and of course it's hard to check. The attitude of catholic priests is based upon the notion that it is saving the child's soul, so unless your turn up wearing a star of david or a turban, I would doubt they'd press you on this.
Quite different to marriage, where I observe the degree of christianity required to use the facilities is a function of the prettyness of the church.
At the most recent baptism we godparented at, became clear that only the grandmother, priest and us out of about 40 people had any real idea of what was going on.