Marriage is not a right...
As per SCOTUS, marriage is a fundamental civil right, it is so fundamental that even inmates, convicts, child abusers and wifebeaters have a right to it.
but leave marriage in the hands of the churches and religious institutions...
Don't forget that there are religious institutions and churches that support marriage equality, so in fact same-sex couples would still be able to get married. And currently their religious freedom to define marriage as their see fit is being impinged upon by the state.
But you will not see support of this from many of the 'gay rights' activists,... because it is not about equal treatment under the law... it is about advancing an agenda
I don't think you will see much support from religious groups for this either because their goal is about enshrining discrimination against gays. They don't want them to have access to civil marriage. It's only a matter of time, and like other forms of discrimination that the majority of Americans supported, most of us look back and wonder why it was an issue.