Gorsuch came down hard on Bostock, which makes me think he’d be skeptical of overturning Obergefell (which he wasn’t on the court to rule on originally).
Roberts is married to process well enough that I don’t think he can find it in himself to violate stare decisis on a case he was actually chief justice for, even if he did vote against the first time. Plus a lot has changed since 2015, and the court took a hard swing right. The dude has always kinda been that middle man referee, so I think that’s another drop in the “would shoot this down” bucket.
That only leaves Alito, Thomas, Kavenaugh, and Barrett. Alito and Thomas will always vote for the craziest possible position, so they’re right out. Kavenaugh and Barrett are more of a coin toss, but I lean towards them having their own, separate dissent if Bostock is any indication (which Kavenaugh dissented on, but not with Alito and Thomas. Barrett had yet to join.)
So my gut is that this isn’t going anywhere. I’d honestly be surprised if the supreme court even took it up.