well... there were many hints and all throughout the story that might insinuate that he might be in that closet, most common thing for guys who are in denial and hardly in a closet, afraid of their gay side, is chanting all the time that they love girls and girls only.
I get that others might think different etc, I read him as bi, but gender or sexuality does not define who someone is from a moment when they come out etc.
Tho about okama island I would more say that they love make overs and drag a bit too much...