Lets look what Burnham actually said on this most recently:
However, at his campaign launch on Friday he said: “I think the time has come to take the Supreme Court ruling and the guidance, and implement it, but to do it in a way that protects those spaces but does not marginalise already marginalised communities, that’s my view.
“My mum and dad brought me up to live and let live. I think Britain needs to get back to a more live-and-let-live approach to life, not where we’re constantly arguing with each other, being judgmental about each other.
“Let’s implement the guidance, but do it in the fairest and most compassionate way possible.”
He also said he thought Britain had done too much re-running of arguments.
“We’ve got to stop arguing with each other. We’ve got to start by finding some common ground and start pulling together,” he said.
Andy Burnham has backed single-sex space guidance and said the Supreme Court ruling on the definition of a woman should be implemented
https://archive.is/VHOdW#
What do we see here.
Burnham thinks like Starmer that this is all a fuss about nothing fundamentally. He doesn't care about women's rights BUT neither does he care about the trans line. That is why he has reversed his position. He never cared in the first place he was going along with TA stuff as it seemed the easiest course. The biggest emotional cue is -
HE WANTS IT ALL GO AWAY.
So I don't think we can look to him for an ardent defence of women, but also do not underestimate how little he wants to be arguing with Kemi and Farage what a woman is. He also can see trying to fight women on this issue is not going to be easy. Given he never cared why spend the effort on it.
Of course Burnham may be hiding his fanatical supports for gender issues, but the stuff he said years back has no substance it .is just repeated TA lines. We are not talking someone like Whittome who clearly believes it.
His change is because a bunch of people mainly women have defeated the TAs in court again and again. Burnham can see women have taken their power back, he is in no hurry to fight them. He admires the biggest gender crit in government Shabana Mahmod by all accounts.
Look what has just happened to the SNP they lost their 4th court case against women. Why would Burnham want to try something so dumb?
Plus accepting the court judgement and letting the guidance be enacted puts a safe distance between Labour and the Greens/Lib Dems/Plaid/ SNP who still want to continue trying to take women's rights away.
The Manchester mayoral election will be Labour vs Greens and Reform. We can expect Burnham to move against Greens heavily during that. I think sex/gender may come up in the mayoral race.
It doesn't mean we trust Labour. There are still TAs in there. Especially with the so called conversion bill coming up. However we will fight that battle when we get to it. Yet we also need to recognise the landscape has permanently changed. We have won many battles, pushed the TAs back, many more to fight.