This kind of thing is going way too far.
At some level, I can understand the removal of Confederate symbols from public places. It probably shouldn't be part of Mississippi's flag. Statues of Lee and Pike probably shouldn't be in DC - although in my mind that's more because they were traitors to the country whose capitol it is. In Confederate cemeteries, well...that's actually probably an appropriate place for those monuments. In places where both Union and Confederate soldiers are buried, it may even be reasonable to have the two flags flying together - just like we do at other war memorials and cemeteries around the world (although, I believe the WWII German cemeteries fly the German flag, not the Nazi flag...so the argument could go either way).
Where I have a problem is when you start going to individuals and telling them they can't fly a flag, paint the roof of their car, have a tattoo, etc. That crosses a line and is where the threats to the 1st amendment actually arise.
There's a story out of Walla Walla right now that I find troubling for the same reason. A police officer there apparently has a tattoo that resembles the Nazi SS logo - the lightning bolt double S. It's become known that he has this tattoo, and a number of people - including city leaders and the public - have pressured him and the police department to change or remove the tattoo. He has declined, and the police chief has (rightly, I believe) said he can't make him do so. In response, the president of WHitman College today severed ties with Walla Walla PD - saying they won't use them as part time security, police officers can't use college buildings for training, and officers can't use campus fitness facilities, at least until the officer removes or changes the tattoo.
This seems a very dangerous precedent to me, when civic leaders now believe that they can force someone to physically change their body because others don't like it.
The officer says that the tattoo is actually in memory of someone killed in Afghanistan, and he covers it when he's on duty. In my mind, neither of those details is relevant. Even if he is truly a neo-Nazi, if it's not impacting the way he does his job and he's not threatening people...there's nothing the department can do. Even if it's perceived as a form of hate speech, there's nothing civic leaders can do. Hate speech is protected speech, and the courts have affirmed this multiple times. The only exception is if it is intended to provoke an imminent violent response. Neither a tattoo or flag likely meets that standard, and therefore should be protected.