I mean it was a "Let's say he was..." question.
I highly suggest you edit the title to make this clearer and explicitly state that part of this ATL is that Hitler was a homosexual.
Long story short, Hitler wouldn't have been leading the NSDAP, especially by the time this, however it may be gets leaked. Much less Germany.
Considering the cut throat nature of party politics, I'm sure an NSDAP member would have found this out much earlier and used it as kompromat in order to force Hitler to step down from major leadership positions. Paving the way for said NSDAP member's own rise to leadership within the party.
When this is leaked, Hitler is likely some back bencher in the Reichstag. This is still is a major scandal as a member of the Reichstag was revealed to be a homosexual. Hitler resigns from the Reichstag and is publicly kicked from the party.
Given the lower ranking nature of this ATL Hitler, the NSDAP would still easily survive this.
The main question is who would the NSDAP leader and thus Chancellor be in this period. One route is that Himmler would be the NSDAP chancellor during this.
However I think Goering is a far more likely candidate to replace Hitler as leader because of his WW1 service.
Goering would try salvage the situation the best he can. A few days after this leak occurs, Goering decides to claim credit for the leaking(even though he didn't do it). Goering then sends some SA guys to intimidate the newspaper that published it into acknowledging that Goering was the leaker.
Goering would publicly say, that as the NSDAP leader, he has zero tolerance for such actions from a party member, and accordingly took action against him.
For NSDAP members, Goering claiming responsbility shows that he is not afraid to publicly admonish and humiliate members, especially those he sees as a threat. This gives Goering much greater control over the party than he did before.
Behind the scenes, Goering would want to hasten the Enabling Act to get complete control of the country.
The Night of the Long Knives still occur, and Hitler is among those removed.
Certainly, having Goering be the Fuhrer would change a lot of things in WW2. But I do not have the expertise to comment how things go down once the war begins.