I just dislike the visibility of men intruding in female spaces
All that too, however the lady in question isn't a threat and as an Algerian woman has spent most of her life in female only spaces.
There's also two things I've noticed (and may get yelled at for the second point).
Firstly, most of the anti-trans stuff is from boomer women. That's understandable; they had to fight for abortion rights, equal pay and in the UK the right to open a bank account without their husbands' permission. They also had to batle entrenched conservative attitudes and did make genuine progress. The younger generation, the 'Zoomers' don't seem to have an issue with trans matters at all.
Secondly, I've a good friend who is generally a very reasonable person. She does however get really angry about trans issues. One thing that set her off into a rage was when an NHS Trust (the one in Brighton where there are a lot of FTM transmen) published a health information leaflet that referred to "people who menstruate" rather than women and the right-wing media picked up on this. She went ballistic when Rowling, Bindel etc were publcising it all. The thing is, she hasn't menstruated since she had a hysterectomy decades ago and now she's past 70 she's got facial hair, a deep voice and could pass for a man if the lights were dim and she had trousers on.
two are autogynephiles
Dangerous and obsessive nutters. Annoying blokes with tampon fetishes.They help turn the public against people who genuinely don't fit into the gender binary.