I’m not a lawyer. And I don’t play one on TV. But you can file a civil rights lawsuit for a “protected class” reason only (race, national origin etc.). Political affiliation is not one of the protected classes.
And it’s not a free-speech issue. You can’t just say whatever you want on someone else’s property.
But as you said, if the situation ere reversed the ACLU would sue. The lawsuit would fail. But they would try anyway. And maybe Antifa would show up, and break a few windows.
I am not a lawyer either.
But this isn’t someone else’s property. Its a business open to the public.
Its a legal subject which should be pursued in the courts.