You want anecdotes for why some of us have concerns about erosion of single sex spaces? I've known a load of trans people. I'm a geek and they're everywhere in my hobbies. I'll refer to them according to the pronouns they usually expect me to use here, which I appreciate is controversial, but I do this offline as standard so as to not be completely ostracised and lose my job, so I may as well indicate here how I'd usually refer to them.
One was one of my long-term partners, who is an autogynephile, has no illusions about his paraphilias and should very definitely not be in female toilets or changing rooms because it'd be a turn-on for him to see women in a state of undress, and he's a decent person who would be mortified about potentially causing distress or alarm to women or children so would never put himself in that situation. He doesn't engage in his paraphilias in ways that cause harm to anyone (except himself) and has suffered quite some anguish in the past at how his proclivities are doubtless tangled up in subconscious sexism and feed off of harmful stereotypes. They set in when he was young, and have caused him a lot of unhappiness. I'd say he needs therapy but isn't a risk to anyone except himself; if he were predatory or just less of a decent person and decided he wanted to barge into women's spaces or involve unwilling participants in his fetishes, it'd be an entirely different kettle of fish. He broadly agrees with the majority of GC causes and with JKR, although finds her unpleasantly direct.
One of my childhood autistic friends developed a hatred of other men at his all boys school due to horrendous bullying. He declared himself a lesbian as a teenager and started trying to date lesbians without doing any sort of transitioning or even changing pronouns, and seemingly couldn't understand that this might not be something they'd be interested in when I tried to question it and encouraged him to get therapy about his experiences. We drifted out of contact but I heard that he was still trying to date teenage girls as he got older.
Another (post-op, well passing) transwoman I knew through a hobby was notorious for repeated sexual assaults and anger outbursts / violence, to the extent where new entrants to that social circle would be warned about her by the other women. She's very feminine and meek in presentation publicly, but barged past me once and nearly pushed me over. There were men in the same social circle who I was also warned about, and trans women who weren't the subject of similar warnings, so I doubt she was being singled-out due to transphobia.
Another transwoman hobbyist, on one occasion, cornered me alone at a social club in a small room and gave me sexualised compliments whilst blocking my exit. She's built like a rugby player and I was silently having a panic attack whilst I went into fawning mode. I started using the disabled toilet because the female ones were in an isolated building and the club policy was that she could use them, and I got other club members to walk me to my car after events because it creeped me out so badly. She was eventually thrown out for sexually inappropriate conduct towards another attendee.
One of my close friends has a transwoman relative who has been arrested for alleged GBH against their own baby as well as abuse against the mother.
I've also unfortunately known a lot of extremely unpleasant, abusive or outright criminal men, including ones who've been imprisoned for child abuse. This hasn't led me to view men or transwomen as monsters, it's made me see those individuals as bad people.
I've also known plenty of trans people who seem lovely, although most of them seem to have mental health issues, autism and have suffered extremely sexist upbringings.
Campaigning for single-sex services, for accurate data collection, for fairness in sport and the other common gender critical causes doesn't mean I hate transwomen. It means I see them as human and as likely to be a risk to women and children as any other man, according to the biological differences between our bodies, the statistical evidence showing that they exhibit male patterns of violence, and the repeated personal experiences I've had which have demonstrated abusive and predatory behaviours from some transwomen.