I'm at an organization where a similar situation is proceeding through the HR hell.
The unfortunate part is that as an at-will employee, which we all basically are at my job, they have to do something highly illegal to actually get sued for firing you. You can show up and pick your nose and get fired for it, and it's just "at will."...
Now, if they actually said "Because of this" you might have a better case, because then they're stepping on first amendment stuff. But if they said "Because we want to" you'd be SOL. People don't get that your first amendment rights protect you from jail time, not protect you from any consequence at all.