Aaron Hernandez's self-hate for his alleged gay secret is NOT why he turned violent -- so says Marco Rubio.
We got the Florida senator out on Capitol Hill ... and asked what he made of the recent "Aaron Hernandez Uncovered" documentary, since he and Hernandez share the same alma mater (Florida).
Marco told TMZ Sports he hasn't had the chance to watch the whole thing, but with that said -- "I don't think that's relevant to killing somebody."
That "somebody" was Odin Lloyd ... a man some law enforcement officials believe Hernandez murdered in 2013 because he knew about Hernandez's sexuality.
Rubio clearly ain't buying that ... but on a related note, told us he sees positive momentum for gay athletes and politics having the platform to come out.