The only one currently on the Court I could see particularly caring about overturning it is Alito. Thomas might but he also might defer to his former BFF Scalia's original ruling on it, and Roberts seems like someone who might've dissented if he heard the original case but now considers the issue settled. ACB I'd say is possibly a tossup between either the category I put Roberts in or opposed, Kavanaugh while a pretty loathsome individual seems to be pretty solid on free speech issues, Gorsuch is way too much of a textual literalist, and none of the liberals are going to be onboard since it seems Stevens' original dissent was a fluke probably influenced by his Greatest Generation patriotism (he was not only the last WW2 veteran but I believe the last veteran at all to serve on the court.)
Thomas was close to Scalia, but he broke from Scalia in many notable cases. Remember
Hollingsworth v. Perry, where Scalia and Roberts cast the deciding votes in favor of gay rights? Under no circumstance would Thomas ever side with gay rights despite Scalia once doing so.