That's a sticky situation...while it's true that his affiliation could raise some trust issues, it's also true that each and every one of us (including the racist in the picture) has a right to freedom of expression...even if that expression is tremendously unpopular (provided they don't act on that and infringe upon the rights of others).
If we leave the group names, and career names out of the equation and just ask the question in generic terms:
"Does a public-sector employer have a right to fire someone for exercising their constitutional rights in their own personal time if they've broken no law and performed their duties correctly while on the job?"
...does it still make sense?
If the answer is yes, then we open up a huge can of worms. I certainly wouldn't want a fireman to be fired for attending a pro-choice rally on their own time, because the public in their area (and their chain of command) disagreed with that viewpoint.
