Now, generally, I tend to believe that if a person is accused of transphobia (or sexism or racism), there is probably at least a molecule of truth there. No one has more experience with transphobia than a trans person so I'd trust their instinct, and most cisgendered people are a little transphobic. Doesn't make us horrible people necessarily, just means we have some learning to do.
That being said, this situation is a little more complex because it involves a bath house in Japan, where the "rules" about gender and nudity are different from how they are in the U.S. The woman who shared the story is 20 years old and currently living in Japan as part of an exchange program. She's there with a group of female friends, including a friend who is a pre-op trans woman. She writes:
I am a 20 y/o girl. I am in Japan on exchange with some friends of mine. Most of my friend group are women, including a 21 y/o trans woman. She was born a male and started transitioning in her teens. Currently she is pre-op and saving up for gender reassignment surgery. However, you can hardly tell that she used to be a male, save for her voice and height/body frame.