If their constituents are split on an issue then yes, they have to make the decision for themselves (and I also agree that they should only make their own decision when this is the case).

Concerning religion, I believe it is possible to form full political and moral stances not based on religion. The gay marriage debate shouldn't be a debate on whether or not it's against the Christian definition of marriage (or sin!), rather it should be a debate about whether or not government-recognised marriage is a basic human right or not. That debate shouldn't have anything to do with religion, rather it's about what's best for our society.