@NekoShiro there is a difference, yes, but an incident (which is completely subjective) can go on your file, to be disclosed if you seek an enhanced DBS.
That has a direct impact on your life, potentially. And therefore there is a chilling effect - people afraid to say what they really believe, even on their own private social media. Which is a problem, given this is a contentious subject, and women's rights are directly affected - you'd need to be stupid or a liar not to see that having spaces where women communally undress affects women, if a man can come out as trans and immediately demand access. Bluntly, there is a claim that a male has a right to expose his penis around naked women, if that male says it's her penis. That affects us. It just does. We have a right to a view on it. Same with sport, and rape counselling, and who is female when we want a smear or a mammogram, and, and, and. We absolutely have the right to express our views, and campaign for the law to uphold our rights to single sex provision. There is nothing hateful about that.
I also note that the hatefully misogynistic things thrown at women with our views are not covered. They are hateful, and clearly founded on hatred of women, but we aren't covered under hate incidents, nor crimes. Hatred of women isn't specifically banned, or monitored. TRAs can say whatever they want to us on our sex, but any response along similar lines relating to gender identity would go on your file as a hate incident. While I would regard anything as hateful as their words to us as hateful, yes, so that would actually seem reasonable, what isn't is the asymmetry.
If the test is completely subjective and there is no right of reply at all, then you could have something against your own file right now and have no idea, and it come up if eg you apply to volunteer for the Girl Guides. It doesn't matter how unfair or unjustified that might be. Trans people have found their efforts to support women's rights, and to recognise the conflict, have meant they've been reported, too.