How do you feel about:
"A homosexual is someone who identifies as a homosexual"
Last time I checked, someone identifying as a homosexual didn't require any change from me in how I treat them.
On the other hand, I have a very clear idea of what they mean by it: They're sexually attracted to others of the same sex.
We still have no clear idea of what "identifying as a woman" actually means (other than identifying as female).
or
"A Miami Dolphins fan is someone who identifies as a Miami Dolphins fan"?
There's a lot of ways to approach this one. Personally my feeling is, "you do you". Again, as long as there's no requirement for me to treat them any differently because of their self-identity.
On the other hand, I know a lot of people take their sports fandom very seriously, and may have strong opinions that a True Dolphins Fan loves or hates certain players, reveres certain games and disparages others, shows up religiously for certain events, etc. But this is all internal squabbling between sects of hardcore fans. It places no burden or expectation on public policy or outsider attitudes.
Just as the third-waves, radfems, and TERFs are welcome to fight amongst themselves about what a Real Feminist is, so too are the trans-inclusionary extremists and radicals welcome to fight amongst themselves about what a True Transsexual is. As long as it stays between them, and doesn't burden science or public policy with absurd religious demands, I don't care.
Note, importantly, that in both cases, a person might engage in certain behaviours and other traits that may be associated with those groups.... without actually identifying as a member of that group or being defined as such.
The convenient thing about homosexuality is that it doesn't really matter what traits or behaviors are associated with it. You're sexually attracted to the same sex, you're sexually attracted to the same sex. You don't need to give your homo-erection a special name in order to enjoy the fruits of its labor with a like-minded individual of compatible sex. And the only demand homosexuality makes on public policy is that public policy stay out of the bedroom.
None of this is true at the current state of the controversy over transsexuality.