The game is fully customizable as far as gender, and I'm not sure if tagging "Gay Straight Lesbian LGBT" helps anyone. But maybe it does?
I know people on some websites like NewGrounds use those kinds of keywords to block offensive content (e.g browsing porn without seeing gay stuff.) I'd hate to see my game blacklisted by people just because it has the option to play with male characters. Nevertheless I think I'll take your advice and add those keywords -- thanks so much!
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Tagging it as Gay and Lesbian does help! I'd say LGBT would be the most appropriate descriptor, but when people search using the tag system they are looking for games that contain that kind of content — not necessarily games that are exclusively about it. So, you know, you'd have a lot of people who'd search for Gay or Lesbian, find the game, and be very happy they found it.
Itch doesn't have a blacklist feature (it's been asked for, but I don't think they want to add it) so that shouldn't be a concern for the most part. As a dev, though, I can assure you that these tags I mentioned bring in a lot more people than they could ever repel. The community of LGBT players on Itch is extremely lively.