I think there is a place for discussing how trans rights will impact on women's rights, without accusing every trans person of being a pervert with a hidden agenda.
As has been said, it's a (deliberate?) red herring to claim that anybody has said that ALL trans people are perverts. What is being gleefully ignored here is dignity: the fact that women do not want to be forced to be in vulnerable positions in front of male-bodied people.
In fact, most men also don't want to be changing or going to the toilet in front of women either - even though very few of them would actually be at risk from any invading women. It's a long-standing common-sense part of our human culture that we keep separate facilities for men and women in intimate settings.
The main issue is that there is already a clear immutable way of deciding which people are allowed to use which facilities, and it is one that the vast, vast majority of people have understood and been very happy with for a very long time indeed. It's irrelevant if somebody feels that they should 'qualify' to use a facility that is not appropriate for them, just because they feel that they should.
I could genuinely feel like I should be an accredited Gas Safe engineer - and identify as such - but it doesn't mean that I should be allowed anywhere near people's boilers. The difference there being that I could train and qualify to do that job, whereas it is clearly a biological impossibility to change sex - which everybody deep-down does know, but the 'gender' word is deliberately used to blur reality.
For those who don't understand, 'sex' is unchangeable biological fact - and the yardstick by which we decide who can access which toilets, changing rooms, sex-based sports, prisons and many more facilities. 'Gender' is how people feel, identify and choose to behave socially, which is absolutely fine for them to do, if they wish (although most people don't 'identify' into a 'gender' at all).
Therefore, just as we don't have separate facilities divided on other personal and social preferences, likes or dislikes - such as for people who like Coronation Street, for people whose favourite colour is green, for people who refuse to drive anything but a Mercedes, for people who use Instagram but not Twitter, for people who are vegetarian, for people who hate classical music, for people who tend to vote Lib Dem........... - we obviously also don't have separate facilities for men who may feel more comfortable dressing in traditionally feminine clothes (which nobody is stopping them from doing), but who are still nevertheless immutably men - for whom full appropriate facilities do already exist - meaning that they have no need and no right to force other (female) people to compromise their own safety, dignity and privacy by being forced to share their appropriate facilities.
Simply put, if everybody is given one cake each, it is patently not 'fair' to demand that somebody else should give you their cake, so that they have none and you have two - even if you somehow believe that you should have the special right to two cakes and thus that they should lose their right to any cake at all.
It's not the best analogy, but this is all a bit like these tiresome people who will happily wave away (other) people's rights to privacy in various spheres with the irritating Orwellian phrase "Nothing to hide, nothing to fear" - suggesting that personal privacy and dignity as a default should not be respected; and even go as far as suspecting and questioning the motives of those wanting their privacy, rather than ever questioning the motives of those openly wanting to invade that privacy.