Levels of casuals:
Level 1 - Hydra are nazis! The movie said so.
Level 2 - Actually the Hydra were founded by nazis in the comics too and many nazi super villains showed up there.
Level 3 - Hydra as a concept was created to reflect a cult of collectivism, the idea was to create a terrorist cell with communist overtones in the 60-70's ran by a office worker who just wanted to be worship.
He preyed into the idealisms of collectivism (Marxism was just one the things invoked by the first Hydra grand leader) so people would adore him and his cult in an almost religion manner.
Think back about the Hydra's motif and catchphrase and they all fit much better than "just a bunch of nazis".
Hydras were originally the red scare menace done in a surprisingly interesting manner and were warped into generic bad guys with some Nazi leaders.