Yes, because the typical SCOTUS justice is an Optimate first and a liberal or a conservative or whatever second.
Anti-Stratfordianism is close to being the thinking man's Flat Earth in terms of the level of support for it, and it says some very bad things about the level of snobbery and deference to the rich and famous in Anglophone societies that we don't see the same sort of theories about great commoners in other literatures like Cervantes (a New Christian son of a barber-surgeon who was briefly enslaved) or Boccaccio (a bastard child of some merchant).
I haven't looked into the matter so I can't comment with any great insight. However it seems possible to me that they are not so much projecting their own snobbishness but trying to apply the norms of English society at the time. Or perhaps it is the judge's more discriminating eye for detail shining through? I do not know.
Historically England has had a rather less hierarchical and illiberal society than, say, France. Do not Shakespeare's origins actually speak more about "Anglophone society"* than some critics'? Molière and Corneille did not have humble origins. And if all reputable people dismiss the Oxfordian theory what is there to complain about?
*A frankly idiotic phrase which could have come from a narrow-minded Frenchman, given how different Britain and America are; especially on issues of class.
I'm not particularly invested in my hot-take "cultural" interpretation above so I'm happy to concede to your refutation of it. I am, however, committed to the view that the popularity of anti-Stratfordianism among groups of people like the federal judiciary says more about attitudes towards class and its relationship to artistic talent
among those groups in particular than you seem to be arguing it does.
I also don't at all agree that it's "idiotic" to treat the UK, the US, ANZ, etc. as a sociocultural unit, at least for some purposes. Whether this is one of those purposes or not is, again, something I'm happy to concede for now.