There are no LGBT characters in OMORI, unless you count Captain Spaceboy, a character created by Jami Lynne. He intended for Captain to be trans, although this is never confirmed, mentioned or even suggested in the game and OMOCAT most likely did not know this about the character.

Game's themes aren't woke or left-wing. Christian Church isn't depicted as evil, there is no misandry/pro-feminist messaging. I'm not sure about the Last Resort & Jawsum - I think there is an anti-capitalist narrative in this episode, but maybe it's me being too delusional. In general, game focuses on family themes and friendship instead of political messaging.