Ok, here's my attempt.
Lots of trans people just want to live peacefully and get on with their lives, but a vocal group of transactivists are intent on changing laws (I believe to the detriment of women) and silencing any objection.
Currently the majority of trans people are male to trans (MTT). Most of us still think of "trans women" (TW) as transsexuals - committing to "living as a woman" (whatever that actually means), taking hormones and having surgery. Actually 70-80% of TW don't have genital surgery - most retain functioning penises. As the moment to get a gender recognition certificate (GRC) you have to have lived as the opposite sex for a period of time, and been through medical services - ie: there's a level of commitment before a man can legally be considered a woman. Even then, services are still able to be woman only where relevant (for example, rape crisis centres)
Increasingly trans doesn't even mean attempting to look like or pass as women, it just means an ill defined feeling that you're a woman. I'll attach some photos.
A change in the law has been proposed (and already enacted in 4 countries) which means instead of there being any external or medical validation, you just fill in a form in the Internet and bingo your sex is changed. Also there will be no "get out" for services based n sex. That's all - fill in your form and any man can have access to any previously sex segregated space - prisons, hospital wards, showers, changing rooms, DV shelters - anything.
Th only study of its kind (followed every post op TW in Sweden) showed that TW commit crime, including violent crime, at the same rate as men.
So for all these reasons, some of us are very concerned and are standing up to say that "woman" is not a feeling, and that places segregated on the basis of SEX should remain so, and not based on "gender identity".