So, judging from the posted customer service responses, it sounds like M&S believe they still have separate men's and women's changing rooms but now officially allow access on the basis of gender identity.
And the person featured on the LBC programme is one of the rare few males identifying as trans who is actually medically transitioning.
Regardless of whether they pass or not, a post-op transsexual is who most people think is being discussed in these contexts. And certainly they are often featured on stories like this. It's almost like we are meant to continue in this belief.
However, the new dogma has now gone beyond "a person does not need to have gender dysphoria to be trans" to "a person does not have to present in a gender-non-conforming way, change names or use opposite sex pronouns to be trans". All that is needed is to utter the magic words "I identify as..."
So, meet identical twins Arthur and Oliver. They're strapping, handsome guys. Six foot two, buff and sporting the best hipster beards you've ever seen away from TRA Twitter.
Neither twin has any respect for women.
Oliver goes to the women's changing room and demands to use it. They turn him away. He's furious but there's nothing he can do. Even M&S still say this is for women, so not for him.
Arthur breezes up to the changing room and demands to use it. Staff tell him it's a women's changing room. He nods sagely and says "That's why I'm here. I identify as a woman."
Now what does the staff do? This isn't what their training said. Remember the Glasgow Life staff? They had clearly been advised at the very least that only those males with crippling gender dysphoria would ever seek to use the women's, but most likely got the whole spiel about the need of medically transitioning persons to use opposite sex facilities.
But this as I said is now dogma - no changes needed, no proof of actually identifying as trans. (If you don't believe it, check out the Scottish law about gender representation on public boards. Its provisions beautifully reflect the new dogma. Or the "transphobic" incident at Glasgow Conservatoire. )
Arthur looks exactly like Oliver who was turned away because he is a man. So is Oliver, of course. But turn him down and you're transphobic.
No one needs to demonstrate any proof of their gender identity at all. None. You are to take them at their word. Nothing else but magical words. And no one has ever used words with less than the truth falling from their lips.
That's where we are. Men can utter magic words which are not to be challenged. Women can provide evidence galore for why they need female-only spaces and nobody cares.