She lost because whilst she can believe what she likes, she can’t then refer to a person with a GRC as a sex they do not wish to be referred to as. In other words she cannot ignore the real world enactment of the GRA.
The judge stated you don’t have to believe that people can literally change sex to respect someone’s transition.
Did he say that? This is from the judgement:
I consider that the Claimant's view, in its absolutist nature, is incompatible with human dignity and fundamental rights of others. She goes so far as to deny the right of a person with a Gender Recognition Certificate to be the sex to which they have transitioned. I do not accept the Claimant's contention that the Gender Recognition Act produces a mere legal fiction.
The Claimant's position is that even if a trans woman has a Gender Recognition Certificate, she cannot honestly describe herself as a woman. That belief is not worthy of respect in a democratic society.
He seems to be saying that not believing that someone has changed sex is 'incompatible with human dignity' and not worthy of respect.