Sure, and personally I probably wouldn't play a trans person, I don't know very many (I know like, 3), and I'm not real well-learned on it, I would also question if it was something that would add to the game for me. I don't usually play people of color (being quite possibly the whitest person I know) for largely the same reason: I don't know it well enough to make it a meaningful addition to the game.
Oh, and to add: everyone fits some stereotypes, so while I try to avoid completely stereotypical behaviour I try to throw in a couple tics here and there. Take one of your table players: she's a painter/exterior repair person, she owns her own painting/siding biz, often shows up in paint-stained t-shirts and jeans but sometimes she shows up in a corset and heels. Why? Because she likes to.