I doubt Gorsuch votes to overturn Obergefell, though his reasoning might be different than Kennedy’s.
Banning gay marriage is straightforward gender discrimination in the exact same way that banning interracial marriage is race discrimination.
There are a couple points here that make a distinction, though; first of all is that the Fourteenth Amendment doesn't specifically list sex discrimination (or any other kind of discrimination) as banned the way Title VII did in the language ruled on in
Bostock. There are some debates as to whether or not the Fourteenth Amendment bans sex discrimination - this is a major part of the debate over the ERA - and I believe Justice Thomas has stated at least once that he does not believe the Constitution prohibits sex discrimination at all (I may be misattributing a quote from another jurist here, though). Even without that, though, the specific text Gorsuch cites to make his argument in
Bostock doesn't exist here except in previous Supreme Court precedent, and Gorsuch himself is generally more open to questions of original intent when dealing with the Constitution itself when compared to statutes where he almost always goes for the grammatical, plain-meaning approach.
Also, the specific precedents of the Supreme Court here present the other major difference, which I think Roberts and Alito (maybe others) relied on in their dissents in
Obergefell - that though the court has recognized sex discrimination as being barred by the 14th, their precedents indicate that a lower 'intermediate' scrutiny standard should be used for it, whereby sex discrimination can be carried out by the state if it has a very strong government interest to do so - if this standard is accepted then you have to deal with questions in that direction.
This scrutiny standard hasn't always been applied uniformly; at times it's been used pretty closely to strict strutiny, and if a hypothetical case came before the court it's possible Gorsuch/Roberts/Kavanaugh/others choose to do something like that just to nip the issue in the bud (assuming it's even allowed to come before the court at all ofc), but from Gorsuch's perspective/legal approach specifically it takes more work to reach the conclusion of
Obergefell than it does that of
Bostock.
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