HL came to a different view. Lord Nicholls was reluctant to acknowledge that a man can literally become a woman. He was wrong about that.
But Parliament has legislated on this and produced the GRA.
Other parties rely on Elan-Cane. That was about requirement to state sex on passport as male or female. Court found no violation; didn't consider the GRA. Now we have the GRA, things are different.
It's not correct to say that sex is immutable and that's reflected in the law.
Schedule 3 to the EqA provides exceptions, but that doesn't mean sex is immutable.
I guess "literally" now means "I've written it down on a form".