Something that perhaps doesn't get enough attention is that, although it might be nice if everybody liked everybody, or at the least, nobody systematically disliked people because they have some protected characteristic, doing so is not illegal.
I'm loath to choose a particular protected characteristic, but for the sake of argument, let's suppose that climate change denial is considered WORIADS and hence is protected (I don't know whether it is or not). I'm within my rights to strongly disagree with that view; to dislike people who hold the view; to avoid ever making friend with someone who holds that view, and to drop someone like a hot potato if I find out they hold that view.
What I'm not allowed to do is harrass or victimise someone (in any context) for that reason; or discriminate against them for that reason in a broad, but defined and limited, set of circumstances laid out in the EA2010. That set of circumstances includes provision of public services, education, employment, etc., but it does not include private life. If I say to all my friends, or even, I think, in a TV interview I do in a private capacity, that I think climate change deniers are idiots, IANAL but I don't think the law can touch me. If I say it in a widely reported TV interview then maybe there might be a case that it's not possible for me to avoid discriminating against climate change deniers at work and a case might be brought on that basis, but I think (lawyers please do chime in) that it would make an interesting case, if I said "yes I think that but of course I leave my personal views at the door when I arrive at work" and if nobody could prove otherwise.
Basically wrong think, even telling people about it, is not illegal and it doesn't have to be WORIADS i.e. legally protected wrong think, though of course it helps if it is! People are legally allowed to think awful things and even, mostly, to say them.
None of this is to say that SP has anti trans beliefs beyond the obvious basic GC ones - but if my understanding is correct, it doesn't matter if she does.