None that differ to anyone else. The rights trans people are due are the rights to go through daily life not being hated or aggressed for being who they are. Some of the rights they ask for may arise from a need for safety - such as changing rooms, loos etc where they are not liable to attack and ridicule. It's not hard to see that this might be desirable or necessary. But it should be obvious to anyone within the trans movement that this need and right cannot and never should jeopardise or eradicate any existing women's rights.
So, that does not include access to female safe spaces, female changing spaces, jobs that are sex-specific for reasons of safety, such as rape crisis counselling or refuges, or the right to compete in female sports.
The point I was making - not clearly enough - is that the trans rights movement would have a lot more support and respect if it recognised that perverted and misogynistic men, men who are not genuinely trans at all, manipulate the trans movement to abuse women with impunity. And the trans movement needs to root out such men and take steps to prove it has no allegiance with them.
Genuine transwomen need to stand together with biological women and recognise this. (By genuine transwomen I mean those who are not perverts, don't get a kick out of flashing their lady tackle in female changing rooms, and don't want a sporting gold at all costs etc etc - yes, they exist - ordinary trans people who just want to go to work, see their mates etc without hassle, they just happen to feel right in themselves if they present themselves in a way that the majority of people would read as feminine not masculine.) If they worked with women to figure out a fair and harmonious way forward, and if they valued and listened to the different needs of women and recognised them to be as valid as their own needs, then the hostilities would ease off. Hostility slows progress. Communication and respect speed it.