He's allowed to ask questions as long as he's not wearing a CF uniform slash openly stating "I am a CF member blah blah blah."
I don't see anything wrong with a CF member taking part in peaceful protests/demonstrations/etc., as long as they aren't in uniform or openly stating they are a CF member, and if the CF does it isn't reflected in the QR&Os. Is it a good idea? Probably not, because things can go awry and you're setting yourself up to be in the wrong place at the wrong time, even if you didn't do anything wrong.
Also, I'm not a white supremicist, nor would I attend a "white pride" parade, I think it's quite stupid, just like I think a black pride parade is stupid. But I am a bit offended that there are gay pride parades, black pride parades, "insert random thing here" parades, but a white pride parade is expected to be met with violence.
I can't speak on the Hitler and Mussolini quotes, but a CF member shouldn't get in trouble for attending a white pride parade if a CF member isn't going to get in trouble for attending a black pride parade, and I'm quite sure we recently authorized members to attend a gay pride parade in uniform.
-Addition, I heard about wearing uniform to gay pride parade, in fact my some of my good friends were asked to by the CoC and we had humourous remarks since these guys weren't gay.
EDIT: Was not under the impression that multihobbiest meant his questions were about white supremacy in the CF and his fireteam partner... Might be the green beers kickin in.