'Gender identity' seems to have become a really nebulous term, deviating from older conceptions of it as a self-awareness of one's role as either a man or a woman and that self-awareness being apparent in everything a person does to indicate that he or she is male or female.

If gender identity is just defined as one's own personal sense and nothing more, then it doesn't seem possible to disprove. Previously it seems like personality and physical characteristics and behavior and interests were all supposed to be one's gender identity on display, which is why with 'gatekeeping' people without evidence of that in their lives and personal history would not be approved for transition-related treatment, because their unconscious gender identity does not indicate cross-sex identification, or a gender identity disorder.

So it seems like gender identity as it is defined in more contemporary times is unfalsifiable, but by earlier definitions it would have been easily something one could prove or disprove.