What matters is what people have been saying from the start - that women who (for whatever reason) do not want to share personal space with men/people with penises have the right to refuse to do so. Also that we should not be gaslighted into not exercising our right to refuse because we are unaware that the transwoman is actually a man/person with a penis.
If the law said that female spaces should not be used by men/people with penises, none of this would be an issue. Men who want to identify as women but don't want surgery could simply stay away from exclusively female spaces, and when the concern about their being there was removed it seems to me more likely that they would be able to go about their lives as women with far less hassle.
As has been pointed out, transpeople have been around for a long time, and on the whole they have simply blended in. What we are seeing now is not about that at all - we have a group of people who are so vocal about the issue that they are making the lives of 'quieter' transpeople much more difficult and are silencing (or cancelling/no-platforming) anyone who doesn't agree with them and let them do 100% what they want. Many of these people do not want to 'live as a woman' in the sense of assimilating into a more female way of life - if they did they would not wear beards, or present at beauty salons asking for genital waxing.
I don't know what is so difficult about people with penises staying away from female spaces, which are few and far between anyway. I can't remember the last time I was in an excessively female space myself, and I am a woman who was born female. If I had to go to hospital, however, I would not want to be in a mixed ward, and I don't want to have men/people with penises in the female changing rooms of a swimming pool, for instance.
What I can't understand is why men/people with penises would want to be there, and why they wouldn't understand why their presence would be worrying for a lot of women. My husband and son would fully understand this, and it wouldn't occur to them to impose themselves where they would make others uncomfortable.