No, it means that states must have a pretty good reason for treating aliens differently, but the fact that an act which would otherwise be within their power is federally prohibited when targeting citizens but not aliens—the outcome of a Privileges and Immunities basis for incorporation rather than the more historically common Due Process one—may itself be sufficient to allow a distinction.

I mean, your basic argument is that Thomas is just pointlessly making semantic disagreements with the majority that would have no effect on this or any other conceivable case because either basis for incorporation produces exactly the same result not only on the present case but all possible cases. While I have a low opinion of Thomas, it's not quite that low.