It's about a tiny minority making an overwhelmingly larger majority feel uncomfortable. It's about one trans woman in a female facility making an eventually much larger number of women there feel uncomfortable.

Men talking about women. The number of women who will be upset about this isn't as large as you think. And it may be more difficult for the more masculine men to do the transition easily. I think the more feminine men will be accepted readily.

Our country does have rhetoric in the past about the "tyranny of the majority" but in a different sense. We have 11 different cultures (at least), and more subcultures, plus rural vs. city. My guess is a trans will head to the city and denser urban areas, where they won't stand out. Some places in the country may take a very long time to transition toward acceptance. Germany is the size of Montana. The US is as big as Europe all the way to the Russian borders. Some of our cultures are less accepting than others. It's never easy.