I believe the statement by the restaurant is false on its face. They must have decided, with the help of their lawyers, that saying "We won't serve them because we don't like their political views" wouldn't fly.

Accordingly, I would not rise to the bait by trying to refute the argument made. Rather, I would address the real reason for the refusal - management's opposition to the group's political views. That seems to me a harder moral case to sort out, although the law regarding public accommodations may govern the legal aspects of it.

Public accommodations like restaurants are subject to closer scrutiny of their discrimination than are individual artists. That alone may distinguish the restaurant case from the baker and the web designer. Also, I am not among the "we all" who can agree on those cases, so arguments based on inconsistency with those cases fail for me on two counts - the public accommodation angle and the assumption that the baker and web designer may not discriminate.