On the OP's original point, I'd say we have a Venn diagram of two overlapping circles.
One is people whose pre-existing mental health issues find an expression through trans gender identies because that is a dominant narrative in the current cultural climate.
The other is people with disordered ideas about sex, gender and possibly also sexuality that they project onto others then see reflected back as real. Within that group we have the sexual fetishists whose perception of "women" has become entirely sexualised, and the people with deeply internalised false narratives about men and women that lead them to genuinely believe their personality is incompatible with their sex. What links them is their identity relies on a projection of their own ideas about the opposite sex.
Of course the two circles overlap very much and the overlap increases as the trans identity deepens. The disordered sexist's mental health sufers as they become increasingly isolated through their need to impose control over others and their distress at being challenged and rejected causing them to reteat into embattled communities of like minded people which increases the isolation and paranoia, while the mentally distressed person cannot express their identity unless they create/accept mental differences between the sexes to give them something to identify into, which then become fundamental to their ideas about men and women.