They don't need to consider whether DU's belief is protected to determine whether he had a right to be in the changing room. His belief cannot give him that right, even if it is a protected belief. All the protected belief would give him is the right not to be discriminated against. The comparator would be a man who does not have that belief. They are not allowed in the female changing room even if they want to be there, so excluding him from the changing room is not discrimination against him on the basis of his belief.
He may be able to argue that refusing to allow him in the female changing room is discrimination on the basis of his gender identity, but that wouldn't raise any question regarding his beliefs.
Even if he does have the right to be in the changing room, his presence there when SP is getting changed could still be harassment.
I'm not saying that the tribunal won't rule on whether his belief is protected, but I don't think there is any need for them to do so to resolve this case. If they do rule on it, I would expect them to rule that his beliefs are protected, but that doesn't mean that any manifestation of his beliefs is protected.
Someone up thread suggested that protected beliefs are the law's way of saying "you do you". That's pretty much right. You can believe almost anything you want and you can't, in general, be discriminated against for your beliefs, but that doesn't mean you are free to act on your beliefs.
In DU's case, he is free to believe he is a biological woman and all the other ludicrous things that he said in his testimony, and no employer can discriminate against him for holding those beliefs (assuming they are protected). However, that does not mean his employer has to allow him to use the female changing room or any other single sex facilities. It does not mean his employer has to allow him to carry out intimate examinations on women.