The problems begin when religous issues spill over into the civil arena. The religious right lobbies very hard in State legislatures on such issues as adoption of children by gay couples and of course, gay marriages. It seems to me though that their are important differences between the civil and religious perspectives. Marriage is one those areas where there are both civil and religious laws at work. Each Church has its own ideas on what constitutes a valid marriage, but they generally recognize marriages performed by other religions, kind a reciprocity agreement.
Churches also recognize that the State has a role to play.
You must have a marriage license issued by the State, although many States recognize common law marriages, which are just two people lving together. A judge may perform a wedding that is as legal as a church wedding. When a relationship ends, the same intermingling of religious and civil laws prevails. The Catholic Church does not permit divorce. The State and most of the other religions do.