@OldGardinia
A specific persons choice doesn't matter in itself - that would just be freedom of expression. The issue is the social enforcement of their choice on others. You must respect their pronouns, you must give them access to your space, you must not be critical of this group as a group, and so forth. A specific person's desire to wear a dress is neither a Right Wing nor a Left Wing thing. What is Left Wing is when the State steps in to control how that is handled. Again, simplification but Large State, present in all aspects of our lives is at one end, Individualist 'I look after me and mine, society is managed through voluntary individual action' is at the other end.
I agree with most of this, but you seem to be equating left wing with authoritarian and right wing with libertarian. Left wing doesn't have to mean authoritarian. Left and Right wing are normally used to refer to economic policies. People who agree with high taxation and generous welfare payments may have a whole range of views on other issues. So there are at least 3 strands to this - economically right/left wing, socially conservative/liberal and authoritarian/libertarian.
I agree that a man putting on a dress and saying his name is Sheila isn't a right or left wing thing. It's what happens next that's important.
If 'Sheila' is able to walk around the streets and go about his daily life as he wishes, this is due to society being socially liberal and allowing freedom of expression. This isn't a right or left wing thing. Social conservatives might have a problem with this, but they might be anyone from the religious right (in the US) to sexist people (who could be of any class or political allegiance) who think men should be real men and a man in a dress is someone to be mocked. Many working class people who vote Labour are socially conservative in this way.
'Sheila' now wants to join the women's swimming group and use the women's changing rooms. Social conservatives may obviously object, but I would also expect socially liberal people to consider the impact of 'Sheila's' freedom of expression on others. It's the old 'your right to swing your arm ends at my face' argument. This is what seems to be missing from the socially liberal view at the moment. People are equating the right of someone like 'Sheila' to walk down the street without being shouted at or assaulted with his right to impose his self-described identity in other situations where women and girls are negatively affected by it because they don't want to see Sheila's penis or for a man to see them in a state of undress.
Balancing of rights like this isn't a left or right wing thing, but the left seem to have forgotten about it altogether. In their haste to 'accept diversity' they seem to have forgotten that women and children also have rights.
Taking it one step further, we get to the enforcement of Sheila's right to be viewed as a woman and this is where the state steps in. In the UK both the GRA and the EA were brought in under Labour, but all the social enforcement that has occurred since 2010, like pronouns, has happened under the Tories. They've done nothing to stop this.
The way I view it is that the government is just allowing social changes to happen (which is a libertarian attitude), because they believe this has nothing to do with the state. The problem with this is that it is allowing a sort of non-government driven authoritarianism to flourish. A social media and Stonewall-driven authoritarianism. As though what is happening socially has nothing to do with them. Their libertarianism is resulting in another sort of totalitarianism.