I personally think Gus and Max were gay lovers. But whether or not they were is really irrelevant because I believe Gus took Max under his wing for a different reason.
Specifically, Gus was showing the same kindness that Augusto Pinochet showed him as a young man. I believe Gus was the Chilean dictator's protege many years before, which is how Gus got the nickname "Generalissimo". When Pinochet was ousted in 1988, those close to him changed their identities to avoid prosecution.
Augusto's protege adopted the name Gustavo as a covert homage to the man who showed him such kindness. That's why there's no record of any Gus Fring in Chile prior to 1989.
EDIT: Someone noted elsewhere that Hank mentioned finding records of Gus Fring's entering Mexico in 1986. If so, perhaps Gus went there as an emissary for Pinochet, who was reportedly involved in drug running. Either way, I suspect Gus adopted the alias as an homage to his benefactor.