Transgender people are very well protected in this country against discrimination in employment and provision of services so as far as I see it, the trans rights under threat would be to be able to access women's spaces with impunity as though they were actually women and access to hormones, surgery etc as though it were priority, life saving treatment on the NHS. this includes the social transitioning and medicalising of children.
So why don't they implicitly say this? This is what they want. However it is dressed up as 'we just want to live our lives' 'we are being excluded from public life and public spaces' 'you tell us we don't exist' etc which all sound dreadful at face value.
I think anyone hearing these mantras and putting it together with the narrative that trans women are the most abused, maligned and vulnerable in society are going to immediately think that trans women are instantly harassed and hassled in a public place which is unacceptable. But that's not what it means. It literally means that when they go out in public they want to be able to use the ladies loo.
Now, women have pointed out again and again how that actually does impact on our rights to use ladies loos. Or changing rooms, etc. But rights aren't like pie, we are told, and it's such a nice neat little mantra that it is repeated ad hominim with no thought to what it actually means.....
The rights of other groups aren't like pie at all. If you put in a disabled ramp for ease of access, it does not stop able bodied people from access - but start saying that people uncomfortable with trans people in their same sex toilets can just use the disabled loo, and you are taking someone else's pie.
The rights of Muslim women to, for instance, wear headscarves does not effect anyone else's rights, but saying a trans woman can use their women only space where they might adjust their head scarf literally takes away their pie.
Same sex marriage does not impede anyone else's rights to marriage, but saying homosexuality is same gender attraction rather than same sex attraction literally takes away someone's pie and replaces it with a completely different pie they don't want.