Are you saying the Nazis were better?

The statement that "the Nazis attempt to use black magic to aid their dying cause. Joining the Allied forces, Hellboy eventually grows to adulthood, serving the cause of good rather than evil" is
false
. Two reasons. Firstly a demon is a demon, it cannot be good rather than evil.
Pssstt Here's a little news flash for ya: it's FICTION!! "False" doesn't apply.
I don't love her.. She kicked me in the face!!

Secondly, what exactly makes the allied forces good and the Nazis evil? There was evil on both sides, and rather more evil on the American side in particular than Americans would now admit to.
The Nazis were in league with a sorcerer who wanted to bring an end to the world by releasing the Old Ones.
Can't stop the signal.

The entire theme of the film is that you can choose to be good or evil, no matter where you came from.
exactly. i wonder if the OP was actually watching the movie. the antagonist's monologue was saying "you're a demon, it's what you were meant to be"
with Hellboy rejecting that with the whole 'ripping his horns' off scene.
Its ridiculous to critique a movie with the argument 'it's not real, so it doesn't matter'

Firstly a demon is a demon
It doesn't really come out in the movies, but Hellboy is half human.
it cannot be good rather than evil.
The entire theme of the film is that you can choose to be good or evil, no matter where you came from.