[vezzy-fnord]

marriage is a religious institution, seems pretty clear.

That's the issue, there is no single definition. Firstly, the practical issues of every religion having different views on marriage that may be incompatible with municipal law. Further, in many countries the religious institution of marriage is purely symbolic and not legally binding. There is a wholly separate category of civil marriage, which is often intertwined with things like contract law and tax law, meaning that the denial of it to certain groups can be construed as discriminatory. Once the state is involved, many bets are off. Furthermore, some jurisdictions have so called "common law marriage" clauses that allow for circumstances indirect to religious or civil marriage, such as a domestic partnership, to be considered legally binding marriages.

I generally support having marriage be privatized and simply be a contract set by N parties that is arbitrated by courts, but your presentation omits crucial details. Moreover, whether the ideal marriage privatization is even feasible under the current disparate laws remains an open question.