Oh, for sure dysphoria is not the kind of thing that can specifically make someone need to be called “xe”. I think it can specifically make someone find it upsetting to be referred to with specifically-male or specifically-female pronouns, though, and my sense is that Jordan Peterson isn’t any happier being asked to refer to someone as “they” than as “xe”.
If both “he” and “she” give someone feelings of dysphoria, then I think it’s rude to require that they pick one of those. Singular “they” works pretty well, it has a long history of use in English, and it seems churlish to insist on giving a particular gender to someone who doesn’t feel like either is right for them.
(In some quarters it is claimed that calling someone “they” whose chosen pronoun is “xe” or vice versa is misgendering them, which seems to me just plain wrong. I can imagine a world where we have different standardized neopronouns for different nontraditional gender identities, and in that world maybe it would be so, but we are not in that world. If someone picks a particular set of neopronouns and considers it abusive to be referred to by other pronouns that have essentially the same meaning as theirs, I think that’s mostly their problem. I don’t think that’s at all common, though.)
 This is sometimes overstated. There aren’t a lot of examples until very recently of “they” being used to refer to a known person of known gender. But there are plenty of examples, including plenty from prestigious authors, of “they” being used when a single person is meant.