You would still have the same age, gender, personality, skin color, etc. and you would be able to speak at least one local language and would know basic information of the era and place. Your family, social standing, and such would be randomly picked.
Back in time if you’re gay? Or trans? Or a woman? Or a person of color?
No thanks.
If you go further back in time you can get back to fairly queer friendly societies
The way your society currently discriminates and segments humans is not universal