I'm not "ignorant about what they go through". I've witnessed it at length first hand. I'm nevertheless unwilling to lie in service to a delusion.
Furthermore, I'm not "consistently argu[ing] with" such an individual, I'm simply refusing to affirm their delusion. There's a big difference between the two.
Regarding delusional disorders: some people consider gender to be fungible and independent of sex. This notion is absurd for any number of reasons. It breaks down under the most trivial application of logic. Even among the tiny percentage of intersex persons with genetic defects (that constitute the only legitimate basis for ambiguous gender), the overwhelming majority accept their assigned sex at birth and live their entire lives as one gender.
In short, whatever psychologists might say to spare a patient's feelings during their "nonjudgmental 'voyage of discovery'", the claim that gender is fungible is wrong, dangerous, illogical, and fundamentally no different than the claim that race, species, or age are fungible. It is a delusion, no matter how dearly somebody wishes to believe it.