The “very specific and unprotected groups” you are talking about are political movements (even if non-mainstream) and hence expressing support for them is just as much political speech as any political donation is. All political speech, even extremist political speech, is protected in the US by the First Amendment, unless it incites “imminent lawless action” (see Brandenburg v Ohio), or one of the other narrow exceptions provided for by SCOTUS’ jurisprudence.

Actually, it is allowed to limit free speech to meet “compelling state interests”, and I’m pretty sure SCOTUS would uphold limitations on judge’s off-the-job speech when necessary to maintain the appearance of judicial impartiality as such a compelling state interest. By contrast, I doubt they’d view limiting the speech of a judicial spouse as necessary to an equally compelling state interest.

Furthermore, unless you are a believer in coverture, Alito’s actions are separate from those of his wife, so once he made clear the flag was his wife’s decision not his, I don’t see how it is relevant. The law does not demand judges recuse themselves on the basis of views of their spouses which they may not share-especially when his wife’s expressive act was not directly commenting on any specific case, at most it was a vague expression of political affiliation-and it isn’t even clear what she personally understands that flag to mean.

> This is a fallacious argument at best and smells of bad faith engagement.

It isn’t a fallacious argument. Rather, suggesting that anyone who disagrees with you is guilty of “bad faith engagement”-that’s a fallacious argument.