Marriage is a legally-binding contract. Since it is in the domain of public law, allowing religious beliefs to support or interfere with it would, in essence, allow the religion to be intertwined with the state itself. So, in my humble opinion, separation of church and state alone would require it to be legal for all people. In addition, just as states can't pass a law to allow for racial segregation of contracts, they can't pass a law to allow for class-based segregation of contracts.

Of course, I am far from a lawyer, and this is a pure layman's point of view.