Actually political parties in the UK are supposed to follow the Equality Act. As Labour found out:
www.equalityhumanrights.com/en/advice-and-guidance/core-guidance-parliaments-politicians-and-political-parties
So the Lib dems are on dodgy ground for sure because their definition of transphobia is not based on the law. Saying transgender people don't exist in the way queer theory claims should not be a problem any more than saying Christianity is a fiction. What you can't do is hassle individual transitioning people or Christians. I mean look at this example it is outrageous in a liberal party:
"Another activist of very many years who is a practising Muslim, was told that he would be suspended from the Party until he had satisfactorily completed LGBTQ+ awareness training, after stating that he had reservations, based on his religious beliefs, about aspects of sex education in schools and about the impact on women of male inclusion in areas such as women’s sports and changing rooms. He refused to undergo such re-education and was eventually successful in appealing against his suspension, though only after more than a year."
Some modern liberals are basically becoming like the Christian People's Alliance party pretty narrow minded.
The problem is trying to turn a liberal party into a bigot party which despises feminists and Muslims is going to run into trouble with ongoing drama. You can see the same thing in the Greens lots of people are fine with people being gender critical which is why they GCs in the party are still a big group.