You aren't less than men. Transwomen are transwomen and that's okay. There is nothing inherently wrong with being male. From my perspective it's a neutral descriptor. You are person who happens to be male. I am a person who happens to be female. But your experiences are not the same as mine. You will only have a male's perspective on womanhood, you will never experience womanhood, just a man's idea of what it is to be a woman and that's okay. This applies in the reverse, I will never know what it is like to exist in a male body.

While I do believe your personal experiences, that doesn't mean they are universal. There are plenty of receipts for the harassment of women and women being assaulted in locker rooms and restrooms especially unisex ones, I haven't seen convincing evidence for transwomen. I am all for gathering more data so we have a more accurate picture of how bad the problem is especially let's say in the United specifically and what can be done to fix it. That transwoman I knew in real life continued using the men's room without incident and he was very androgynous so when I first met him I just thought he was a woman with manly features, but his male socialization gave the game away. He did not psychologically pass at all. I was still polite to him used his preferred pronouns and what not, but he was definitely not a woman and interacting with him was just like interacting with any other man, when I found out for sure he was trans it all made sense. Never once in my life have I met an actual women who behaved exactly like a man. Transwomen though, yes.

https://www.mtsu.edu/first-amendment/article/1594/freedom-of-association

For freedom of association we have a clear distinction between public and private life. Public services, businesses and governments should not discriminate. For example someone who owns and rents apartments should not be able to discriminate against renters because they are trans.

But people should have the right to choose who their roommates are in their private lives. It doesn't matter if you disagree with their criteria, their agency matters and no one should be forced to shared the same house/living situation with someone they do not want to share it with. Some women are comfortable with male roommates, some are not and that is okay. Many non smokers do not want to live with smokers. Some quiet people do not want to be roommates with talkative people. I could go on. That's why people often meet to see if they would be compatible as roommates before allowing the new person to sign the lease and move in. I believe it is an egregious overreach when trans rights activists attempt to destroy this fundamental right of association in people's private lives.

A big sticking point is that I do not believe your claim that you are a woman. Not understanding why women would want women only spaces in their private lives only confirms to me that you do not understand what it is actually like to be a woman. Most men just do not get it. Hence why every blue moon I really enjoy being in women only spaces.

As for being able to request opposite sex services let's use the TSA pat down as an example. It's standard for women to pat down women and men to pat down men. This is a compromise, because most women are not okay with being patted down by a man and many if not most women doing the pat downs would not be okay with patting down men. In this scenario sex matters, so I would say it is not okay to force a female TSA agent to pat down a male body. You should be free to request it, but if there are no women on staff who are comfortable with patting down a male body they should not be forced by the law to do so. (Ideally we wouldn't have these pat downs, but that is another discussion.)