I've said repeatedly that some of these things don't bother me personally e.g. shared toilets but I'm asking questions to try and understand other views, which I thought was encouraged in debates.
If we stick to toilets, then here's the dissonance.
Transpeople want to redefine single sex toilets to be single gender toilets (skipping over the fact they can't define what woman as a gender is). Many women don't like that, you are fine with that. Women who don't like it no longer have a facility to use.
Women want to keep toilets as single sex toilets. This is also fine for you, and for women, but transwomen don't like it. Transwomen use the men's toilets.
Ie. keeping it single sex, everyone still has somewhere to pee, a small number of transwomen are unhappy. If you make it single gender, then women who are uncomfortable sharing toilets with men have no-where to use the toilet.
Do you see where that feels like a problem?
If you look at danger, then it goes similarly, given that men commit most violence:
Sex based - men are at medium risk, transwomen (according to them) are at high risk, women are at low risk, transmen are at low risk
Gender based - transmen are at medium risk, men remain at medium risk, women are now at medium risk, trans are at medium risk (since men are now allowed in either toilet)
ie. by switching to gender based, transwomen are forcing women to increase their safety, to lower the risk to transwomen - literally sacrifice themselves.
And this is all assuming that you take the TRA's assertion of transwomen in the men's being at high risk (which is entirely unsupported) - if transwomen in the mens are only at medium risk, then then nobody is benefitting risk-wise, and women and transmen have increased risk with no justification at all, except that transwomen want to go in the ladies.