I'm not necessarily averse to that in general principle. Although the devil is in the detail: there's a lot of legal stuff tied up in marriage, and undoing marriage as a legal state in entirety would be a massive change to that landscape.Or you can not even have government recognize marriage as a thing at all.
Why on earth make a religion? If marriage has no legal meaning, then marriage becomes pretty much whatever any individual couple wants it to be under whatever conditions they feel like. They don't need to justify it with some sort of metaphysical nonsense (and they don't have to now, nonreligious weddings have existed for a long time).Then, if you don't like that Christians don't consider same-sex couples being able to marry, then you can make your own religion where same-sex couples can marry. The only reason marriage rights were even a thing was because of the government recognizing marriage and it being a equal opportunity issue.
FYI, "marriage rights" and government recognising marriage is basically the norm, as it's been embedded in Western culture since ancient times.