Hydra is a fictional terrorist organization in the Marvel Universe, first appearing in Strange Tales #135 (August 1965), and created by Stan Lee and Jack Kirby, two New York Jews, with Kirby fighting literal Nazis and fascism during World War II.
In Hydra's first appearance, where it was a generic criminal organization, a thinly-veiled SPECTRE knockoff, it was defeated by S.H.I.E.L.D. The organization returned four months later, headed by Baron Wolfgang Von Strucker, a former Nazi officer, and supported by the Red Skull, a Nazi agent. Hydra's origin changed in one of Marvel's earliest retcons, which is fine, as origins are set to change, to overall help better a character or organization's continuity. For instance, Batman initially used a gun, but the character is better now that he doesn't (this is not an opinion, it's a fact).
Since the release of Captain America: Steve Rogers #1, Nick Spencer and Marvel have been adamant that Hydra and Nazis are not the same. But despite many retcons, including one involving Hydra reaching back to snakelike aliens arriving on Earth during Ancient Egypt, the link between Hydra and Nazism was embedded in the organization from the start.
One of the biggest hurdles for the comic book arm of Marvel is the film arm of the company. Captain America: Steve Rogers #1 sold just shy of 100,000 issues, with the second issue selling 66,000 copies. At best, that's 100,000 people being told that Hydra isn't a Nazi organization. Captain America: The First Avenger made $370.6 million at the box office. Slashfilm puts the average movie ticket at $8.61. That averages out to 4.3 million tickets sold. What does The First Avenger have to say about Hydra? It's a division of the Nazi party, led by the Nazi Red Skull, originally started as an advanced science branch for the Third Reich.
While we're at it, the animated TV series The Avengers: Earth's Mightiest Heroes, in season one, episode fourteen, Meet Captain America, Hydra is introduced as a branch of Nazi Germany. In a fucking children's cartoon. In Agents of S.H.I.E.L.D., Hydra is retconned as an ancient religious order dedicated to the return of its banished Inhuman leader Hive, with its current incarnation being the fucking Nazi party.
No matter how much Nick Spencer and Marvel say that Hydra isn't part of the Nazi party in the comics, it's hard to separate the two when more than 430 times of the comic audience is exposed to Hydra being a division of the Nazi party in a major motion picture and multiple tv shows, including a children's cartoon, contradict them.