Agents of STRIKE
HYDRA has always claimed that they were more than a Nazi secret society, and in fact predate Nazism and are barely connected to it.
This is, in fact, true.
HYDRA is based on an ancient secret society that goes back to the Hyborian Age. They are essentially an Inhuman Supremacist cult, that believes that Inhumans should rule the world over regular humans. They seek out a mythical city of Thule, apparently an Inhuman settlement established during the Hyborian Age, which contains powerful sorcery that will enable them to rule the world.
They have been searching for Thule for centuries. It is possible that Thule is just another name for Attilan, the Kree outpost on the Moon that was once inhabited by Kree and Inhumans, or it may be a completely unrelated Inhuman settlement somewhere else, possibly also established with Kree space-fold technology.
HYDRA’s cellular nature keeps most of its true beliefs a secret from its own members, and its membership disagree on the particulars of their ideology. Some, for example, mix their ideas of Inhuman supremacy with white supremacy or Nazi racial ideology (Arnim Zola was a big proponent of this idea). Others care nothing for that, and believe that all Inhumans should unite to rule over others. HYDRA wars among itself as much as it does the rest of the world, which is the primary reason its not far more dangerous than it really should be.