The medically accepted definition of schizophrenia implies specific things that would interfere with performing certain job duties. If you extend the definition of schizophrenia to include stuff outside those criteria like gender identification, then the use of the label to determine fitness for some particular job logically would have to change from "schizophrenics should not perform this job" to "some kinds of schizophrenics should not perform this job." Because you're no longer talking about the same thing.
There is an ongoing effort in psychology to improve definitions, and it constantly wrestles with the conflicting needs of having to assign a label to every patetient's condition, and knowing what to do when that label applies to someone. Having broad labels makes applying the label easier but it also makes knowing what to do harder. That's why the APA is constantly introducing new conditions nobody has ever heard of, like "dysthymia". Formerly that condition would have been considered "depression", but it turned out the conditions people had that used to be labelled "depression", while in a certain sense analogous, had different implications and had to be approached differently.
Transgender people used to be given a diagnostic label "schizophrenia", but if you are familiar with abnormal psychology you'll know that that label was hopelessly vague; it threw in people who "felt" an affinity for a different gender with people who heard voices telling them to do things. These are entirely different things, which is why we now have "Gender Dysphoria".
At one time homosexuality was commonly lumped in with hearing voices as "schizophrenia"; this largely predates DSM-1, which thoughtfully (for the time) gave homosexuality its own disease category. Now that a lot more gay people are out, they seem self-evidently normal, except for their sexual preference.