Leaving aside the question of sports, do you really not see how banning someone who looks feminine from women's restrooms would cause awkwardness or discomfort for that person? If a transgender women is being abused by her male partner, you think that she should be barred from any women's resources or support groups even though she is going through the very situation that these resources were designed for?

Also, what about trans men. Do you feel comfortable with a bunch of bearded men with deep voices in the women's facilities? Or, do you instead think by some sort of double standard that trans men are men but trans women are not women?

I'm sorry, but unless you can answer these questions reasonably then your claim that you have no intention of harming anyone doesn't hold up.