Just to add to the obvious: Ian Curtis was right wing but definitely not meant as fascist, he was just a conservative like many punks, that was a reaction against a Labour government which did rather bad when had the chance to rule, so it was like anything but not Labour again, the movie clearly shows that moment of crisis in England.
The others weren't so politically aware, they were too young to care and just cared about the music.
The whole band was probably attracted to the imagery of the forties, you can see it in the way they used to dress, and certainly deliberately chose to deal with the Nazi element as a mean to make people think.
Just look at the Ideal For Living cover: there's the Hitler youth and there's the Warsaw child surrending to the Nazi soldier. That's not a Nazi cover, it deals with the subject, but so does Schindler's List, doesn't it?
The very name Joy Division refers to the victims of Nazism, a Nazi band would never use that name, they'd use whatever referes to their sick sense of glory.
If Ian ever said "that's us" it's because I read Joy Division also was about the music scene, it compared mainstream musicians to whores, and when you see Top Of The Pops isn't really like seeing a brothel?
Anyway Joy Division not only did benefit gigs for Amnesty International (not quite Nazi) but also clearly chose their place in the music scene, Factory Records.
The culture of Factory came out of Situationism, which is a cultural wing of Anarchism, but politically there was mostly support for democratic socialism.
Durutti Column chose their name from an anti-fascist Spanish leader.
Factory has been, in the whole history of music, the most open minded cultural place, you just had the punks dancing with the black people and their rhythms and you had the blacks pogoing with the punks and their guitars.
You had A Certain Ratio, the most anti-racist band which could ever exist, the perfect mix of the white and black cultures.
In Factory you had blacks, jews, gays and junkies.
In the interviews of the most recent years, Bernard Sumner has supported the Socialist Labour and the Green Party. He's not very interested in politics yet, all he knows is he'd like more social justice and less pollution for the planet where his children will have to live.