Please don't underestimate rape or abuse based PTSD. I am a multiple rape survivor. I flatshared briefly with a lovely woman who kept inviting her new boyfriend to stay over. Despite the fact that he seemed nice etc etc, I used to lie awake at night, too scared to sleep, knowing there was a man in the flat who I didn't know or feel safe with.
Totally my issue and I started looking for a new flat. But in the meantime I put a lock on my door in order to sleep. Irrational? Yes. Overreaction? Yes. Was he dangerous? Very unlikely. But PTSD isn't rational. I never regarded it as anyone else's problem but my God, it was so real. It still is and I've had years of therapy.
Put bluntly, if you have a penis and I don't know you, I am nervous/scared/triggered by being alone with you or in close proximity.
The other thing that I think is really important, is female socialisation. The OPs cousin may well be jolly decent, but in some ways that is irrelevant. Not to misgender the cousin, but until pretty recently they lived and presented as a man.
Lots of men are lovely. But as a sex class, men commit 98% of sexual crime and 93% of violent crime. In the UK 85,000 females a year are raped and another approx 150,000 are sexually assaulted. Very few women have not grown up being catcalled, groped etc. It is part of who we are.
We are not socialised to get undressed around males. We are not socialised to share intimate space with them outside a relationship or family. We are taught to keep ourselves safe, to stick with our friends, to not get in strange cars or unlicensed taxis. Not to walk home alone in the dark, or down alleyways or isolated places.
We are taught all of this because we, as females, have a collective understanding that males, as a class, can hurt us. And often do.
Now, OPs cousin, as I said, is probably lovely. But you are asking a group of women to spend time with someone who, however much of a woman they feel/are legally, is, due to their age and late transition, in all likelihood still identifiably male in many ways and who still has a male body.
Now, everyone there might be A-OK with that. But what if they aren't? Because this isn't just spending the weekend with a bunch of women and a man.
It's a bunch of women and another woman who until 3 years ago, was a man. Who sadly for them (because gender dysphoria must be hellish) probably still looks largely male. And the other women are being asked to pretend that they don't know that. And they at being asked to throw all of that lifetimes socialisation about how they behave around males straight out of the window and pretend it is irrelevant. And that is gaslighting.