They don't 'exclude' in that sense.
I suspect the actual fact is that they represent on the grounds solely of homosexuality, based on sex.
They left Stonewall in order to do this, as Stonewall insisted that they no longer did this as it was exclusionary, and that anyone of any biology was any sex/gender they said they were, and it was wrong for gay people to take biological sex into account.
So the issue of Mermaids et al is that having left to meet the needs of the group whose needs were not being met by Stonewall was evil and wrong and exclusionary.
It's only because they represent on the basis of sex.
And that they don't want any organisation to be allowed to exist that solely represents homosexual people on the basis of biological sex. They want to control and prevent this happening and those people's wishes and needs being met for representation. Even though Stonewall is representing everyone else who is happy to stay with them.
It's the same dog in the manger stuff Sarah is fighting as in 'can I have a female only rape crisis service too as well as the many and multiple options serving all choices of TQ+ people?' and the answer being 'no, you must be unmet and abandoned as to meet your sex based need disgusts us and we cannot tolerate it existing even in a basement at the far end of the town during the hours of darkness'
It's slightly mad.