Nazis have a rich history of stealing symbols and coopting movements. They're like hateful little magpies who steal any shiny bits of culture they find and take them back to their nests to shit all over them.
Most people have differently sized nostrils. It's an interesting physical difference, and there are a few different ideas for why. One is the nasal cycle, and your body simply has a preference for one side, another that you'll hear is (and this is constantly parroted in the EMS world and easily dismissed by the logic that your nose is quite far from the carina where the primary bronchi merge) that your lungs are slightly different due to the heart sitting partially to the left of your chest (for most people), making your right lung bigger and thus blows harder through the right nostril.
Antiracist and leftist is kind of an exaggeration; rather an apolitical subculture of the British working class up until the late 70s/early 80s when the National Front infiltrated the scene. This was during the second wave of the skinhead movement, the original skinheads in the 60s were influenced by West Indian immigrants to the UK, and listened mainly to ska and jamaican music, but generally not very politically conscious or involved. Kind of a rougher offshoot of the mod subculture.
The second wave of skinheads came out of the punk movement. A lot of skins were into Oi!/streetpunk and the NF made their own version which was then called RAC (Rock against communism) but is better known these days (at least in Europe) as White Power Music.
I'm not saying there weren't leftist skinheads (Redskins and Angelic Upstarts would be a good place to start) but as a subculture, the common theme is rather working class identity and pride - which unfortunately, as we've seen, can be exploited by fascist movements as well.