If we can stipulate that "transgender" does not necessarily refer to the mental disorder of gender dysphoria*, then we can stipulate that "transsexual" does not necessarily refer to the mental disorder of transsexualism. Like Orwell said about pacifism being objectively pro-fascist, I'm saying that trans rights activism is objectively pro-transsexualism.
That's the outcome, even if the trans-identifying activists themselves aren't clinically transsexual.**
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*Perhaps some transgender identities carry no more psychological freight than a recreational fursona does.
**They're probably clinically something, though. This deep desire to be seen as the opposite sex, treated as the opposite sex, is either a product of disordered thinking, or is bound to produce disordered thinking, or both.