Nope. One of the manlier characters, Soldier 76... the grizzled war vet.
Going through the list of male characters... I figured they'd go with Lucio or Junkrat for the gay card. But S76 is super-popular, so that's far more newsworthy. Only two "straight white male" types remain.
We're coming to a day where 4% of the population will be represented by 70% of video games/movies/TV/book characters.
Doomfist is black, so they already have that covered. Wouldn't make sense to be gay.
Genji is mostly cyborg.
Hanzo is japanese.
Junkrat is an Australian anarchist.
McCree is an American bounty hunter, a "western" guy.
Reaper is an American mercenary and terrorist.
Soldier 76 is an American soldier/vigilante, generally "good guy", born in rural Indiana.
Torbjorn is a Swedish dwarf.
Reinhardt is a German soldier, heavy crusader-type.
Roadhog is a giant pig-man.
Winston is a gorilla.
Lucio is a brazilian DJ and freedom fighter.
Stop buying the games/movies. They don't make a profit, it'll stop.