It's not about the "dangers of trans people". That's silly, emotive language which demonstrates you either don't have the first clue what our views actually are, or are unaware of the facts (as opposed to your unevidenced beliefs and the cut and paste propaganda you've been told to spout). Do you understand the difference between those two things?
We are probably FAR freer about gender stereotypes here than you people ever have been. Because we don't base an entire ideology on backwards, limiting sex stereotype ideals of so-called "masculinity" and "femininity". You do. Frankly, your views are massively old fashioned to me. Even my grandmother was more "liberal" on that than you people are, and she was born in the first decade of the 20th century. So the claim that you are somehow "advanced" and progressive is utterly laughable, frankly. Your views on men and women are backwards. We ditched them decades ago. That you don't appear aware of that is both tragic and ignorant. You have been misinformed. Most likely, given that your views feed nicely into the anti feminist backlash that took hold in the last 30 years, quite deliberately. It is not a coincidence that you are of the generation that came of age when that was going on, and not a coincidence that you have been strangely misinformed about the facts.
What we are concerned about is the statistical, verifiable dangers presented by MEN. The male half of the population, who, FACTUALLY and statistically, have enormously and disproportionately higher rates of violence, and crucially, for women, sexual violence, than women do. That isn't a "stereotype" because it's evidenced and backed up by the statistics all over the world. These facts are what led to women and men having single sex spaces and services in some circumstances, usually the ones where women are undressed and vulnerable. The reason for this is that while it may be a relative minority of men, women do not know which men these are. They do not wear neon signs saying "It's me." But statistically, for instance, 99% of sex offenders are biological males, and over 80% of their victims are females. "Trans women" I'm afraid make up a part of the biological male group and not the female.
Most crucially, the EVIDENCE shows that "trans people" who claim they are women retain exactly the same crime rates and types as the average MEN. And not, as they would like to claim, as women.
It is not "hate" to point this out. It's THE salient point when it comes to single sex spaces and services.
Why do YOU think that we have those in certain circumstances, and why they are considered globally as crucial for the fundamental human rights of women and girls the world over? Do you understand the reasons?