Douthat's concerns are fair, reasonable, and temperately and eloquently expressed, and for those reasons I commend his piece to your attention.
Ultimately, though, I come down on the other side,* based in part on a truth that Douthat acknowledges:
I suspect that the formal shift away from any legal association between marriage and fertility will eventually lead to further declines in the marriage rate and a further rise in the out-of-wedlock birth rate (though not necessarily the divorce rate, because if few enough people are getting married to begin with, the resulting unions will presumably be somewhat more stable). But these shifts will probably happen anyway, to some extent, because of what straights have already made of marriage.Douthat's post is long, but well worth your time.
* My support for same-sex marriage as a policy matter should not be taken to mean that I believe the United States Constitution requires it.