At my Y I got a membership and I put my preffered name and the correct gender. One of the rules is that men can't use women bathroom and vice versa. I pass one hundered percent of the time. All they know is that my name is Shaun and I'm male. Should it be okay to use the appropriate bathroom(mens) or will they kick me out or suspened my membership?

You should be fine in the mens room, as long as you're passing bro. I think it would be more of a problem if you went in the womens locker room. They would be complaining about a guy in the girls room lol and by your pic, you look male. i dont think you'll have a problem.

If you go by your male name and are marked as male on your club card, then go for the men's bathroom! I think it'll matter more to them that you're in line with your card than anything else. Especially if you have a high passing rate.