The Crescat concern that government recognition of same-sex marriages would eventually force churches to give the same recognition draws on the Boy Scouts and Bob Jones cases for precedents of the government's pushing private organizations into supporting the government pro-equality agenda. However, I think the fear of churches' being forced by anti-discrimination law, or pressured by the withdrawal of funding or tax-exempt status, into recognizing same-sex unions is unfounded.
Consider that despite a long-running public policy against religious discrimination, I still can't get married in a Greek Orthodox church -- or many other churches, for that matter -- because I'm not baptized at all, much less within a particular denomination. Even if I converted to Catholicism and took a vow of celibacy, I couldn't become a priest, despite public policy against sex discrimination, because I'm not a man. (Unless the Church recognizes men who were born as women to be men for the purposes of admission to the priesthood, which would make the Pope more progressive than the Michigan Women's Music Festival.)
The distinction between secular marriage and religious marriage is not new, and same-sex marriage is unlikely to blur it. When the Catholic Church did not recognize marriages that followed a divorce, the government did not force them to do so despite those marriages' having legal recognition. Even after the Defense of Marriage Act, the government has not prohibited any church from giving its blessing to same-sex unions. To require or prohibit religious recognition of a marriage, based on whether that marriage is legally sound, would constitute an enormous breach of the wall between church and state.
The right of private institutions to discriminate on otherwise prohibited bases, when such discrimination is fundamental to their identities, has been well-established and seems unlikely to be changed by legalizing same-sex marriages. Even in the case of the Boy Scouts, Justice Stevens's dissent said that if heterosexuality seemed an essential aspect of the Boy Scouts -- as being a boy is essential to the Boy Scouts, and their sex discrimination permitted therefore -- he would have OKed BSA's violation of New Jersey’s anti-discrimination statute.
Rather than leading to direct government pressure on private institutions, a more probable result of legal recognition for same-sex marriage is that this will increase popular approval of such unions, which is likely to create change from within. Of course, some religious groups have proven more susceptible to such internal dissent than others. Until 1930, Protestant denominations deemed contraception to be sinful, but the growing social acceptance of contraception -- including its legalization -- caused these denominations to change their policy. The Catholic Church, in contrast, has held firm on this issue despite the majority of North American and European Catholics' using forms of birth control other than abstinence. I suspect a similar pattern is likely to emerge if same-sex marriage gains legal acknowledgement.