Hmm, does it have relevance that the guy is a paedophile? Well, in one way no. She almost certainly didn't know he was a paedophile at the time she misgendered him. And even if she had done, you could argue that if the NHS adopts a principle that people have the right to choose their own pronouns, then that right extends to the most unsavoury members of our society, including those who have sexually abused children.
But if you look at it another way, it is relevant, because it shows the utter absurdity and immorality of the NHS's position. Does anyone really believe that this male sex offender believes himself to be a woman? How humiliating to force a female nurse to respect the whims of a man who is so morally depraved. It shows an attitude of contempt on the part of the NHS towards its own staff.
I agree in part with your point about religion. The nurse could have said, perfectly reasonably, that it is factually accurate to refer to him as a man, and that furthermore, it is essential in a medical environment that patients are referred to by their correct sex.
But she might also argue that Christianity is a protected belief under the Equality Act, and therefore the trust is guilty of discriminating against her on two grounds - that of her gender-critical belief and that of her religious belief. So from a legal perspective, it makes the case more interesting. Itf she wins, it opens the way to anyone with a religious belief (including Islam or Judaism) to take legal action against an employer who forces them to comply with gender ideology.