Yes, Jungian psychology has mostly fallen into irrelevance. Concepts like the "Persona" are no longer considered clinically valid.
Trans people suffer from gender dysphoria. It's not a fashion statement, but a psychiatric illness. The treatment for people with gender dysphoria is to help them live in a way that mitigates that dysphoria, such as by dressing according to their gender and finding supportive people in their life who affirm their gender.
Gender is not a product of the persona, but a facet of neurology that is still being researched. There are fundamental differences between the brain of someone who is transgender and someone who is cisgender, and this can be medically diagnosed.
Surgery in this instance is not a cosmetic fashion statement, but a treatment for an underlying condition.
ETA: And, obviously, gender and chromosomal sex are not the same thing. While some trans people are transsexuals and have their anatomical sex changed surgically, this is not viable for all trans people.
Some people experience gender dysphoria no matter whether they present male or female, or else their dysphoria acts in a bipolar fashion where they experience dysphoria presenting female one day and dysphoria presenting male the next day. These are forms of nonbinary gender.
And it is a real, medical construct, even though the vast majority of people are cisgendered.