This whole discussion is quite silly. ISIS laws and tabloid reporters aside, burkas specifically are an
Asian garment, mostly seen around Afghanistan, more conservative areas of Pakistan and India. It was (and still is) enforced by
Taliban. Outside of areas they control, it's seen as a traditional garment mostly worn by old ladies. Western media calling every face-concealing muslim garment a burka makes about as much sense as calling every Western style of formal clothing a suit.
TBH, I suspect niquabs, not burkas were what ISIS actually targeted with the ban. A traditional Saudi niquab+abaya getup (which is presumably what ISIS makes the women wear) looks similar to a Burqua from the distance, but is very distinct. For one, a niquab is a face veil (separate from abaya, which covers the rest of the body), while burka is a full garment. The women who "took off their burkas celebrating liberation from ISIS" either actually wore niquabs, or were so liberated that they decided to go all the way and strip to their undies.
Niquab has been assigned various meanings, but it's not exclusively a symbol of sexism and has stood for many things in the past.
As for islamism and nazism, I'd say they're very similar. Basically, ISIS has fascism with radical islam, while nazis had fascism with white supremacism. Same idea, but with a different ideology. They have the same source, too. A lot of angry idiots, a couple of power-hungry dolts and no strong government capable of either sticking said dolts in prison or lining them up against the wall and shooting them. Say what you will against dictators, but if anyone tried to establish something like that during Saddam's times, the secret police would be all over him in no time.