Covenant marriage---presently an option in 3 states (Louisiana, Arkansas, and Arizona) is essentially marriage 1.0---marriage before no fault divorce. Presently it's used by less than 2% of the population in each of the three states where it is authorized by law.
Since the overwhelming majority of divorces are initiated by women, and most of those aren't for the '3 A's', it follows that covenant marriage supports patriarchy and improves the position of the man within marriage. For this reason even highly secular MRAs ought to get behind it. In addition, because the popular narrative is so at odds with reality (husbands trading wives in on a newer model is actually pretty uncommon but it gets tremendous play in the narrative), it is quite feasible to get lots of feminist-leaning women to join as 'useful idiots'.
Here is a long term plan that would be useful.
Get more states to sign on to the plan. Like the case with CCW, you can point to the existing states that have covenant marriage and have had it for quite a few years now and explain that 'look, the sky hasn't fallen there'. Good places to start would be neighboring states like Alabama, Mississippi, and Georgia. Sure most of your initiatives will fail but you generally only have to win once per state. Seasons where there is a crowded ballot are pretty good too, because your enemies will generally have a lot more fish to fry.
The next step is to get several denominations to push covenant marriage hard in their congregations. Perhaps they could even go to the extreme of only doing covenant marriage ceremonies in their churches.
This is what taking marriage seriously and resacralizing it means.
For a covenant to really be sacralized, it needs to be at least reasonably equitable to both sides. Marriage 1.0 was equitable, and Covenant marriage basically IS 1.0, which is why the hardcore feminists are against it---they see it as turning back the clock on no-fault divorce. They're quite correct, it is a flanking maneuver aimed at precisely that.
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