I think it really depends on a lot of things. Not only the parent's religion and whether I was comfortable with it, but what that religion demanded/asked/required (of me, to help teach the kids) and very much, the children's age.
If the children were old enough that it is very much their religion, and they can do a lot pretty much themselves (things like prayers, scripture study, enforcing dietary/behavior restrictions in themselves for the most part), then I would say certainly I would if they wanted to continue. I'd find a family of that religion to take them to church, I'd drop them for sunday school or youth groups or whatever else like that. I'd learn about their religion, and find similarities between our religions so we could incorporate some things that didn't clash with my beleifs and the beleifs I'll raise my children with into the family, so they don't feel apart.
If the children were quite young, I suspect I could not raise the children in that religion unless it was quite similar to my own beleifs. A baby or a two or 4 year old etc, who I would be teaching/helping learn about the religion, and there is a lot of home based teaching, it's not going to happen. I can't kneel down and pray to the father the son and the holy ghost, or fast for lent, or teach them about the koran, etc. First of all, I don't know enough, and secondly, I wouldn't be comfortable with it. I'm a strong beleiver that you can't effectively raise children in a religion you don't practice and beleive. If their parents were the same religion as me, then of course it wouldn't be a huge issue. I would however, raise them talking about their parents religion (just like I would about their parents and other things about them). If when they were older, they wanted to explore their parent's religion, I'd take them to youth groups/church/whatever, and buy them books, and help them learn about it themselves.
Of course I would want my children raised in my religion by someone else, g-d forbid, however, one has to be reasonable. You can't expect someone not of your religion to raise your children in your religion, imo. If it's really important, then maybe asking someone to be "godparents", who would be very involved in the child's life, so they could help the child grow up in that religion.