Even the law says transphobia is in the eye of the beholder. As are all the other isms and phobias.
Any criminal offence which is perceived by the victim or any other person, to be motivated by hostility or prejudice, based on a person's disability or perceived disability; race or perceived race; or religion or perceived religion; or sexual orientation or perceived sexual orientation or transgender identity or perceived transgender identity.
If the law doesn't consider an objective definition - on which any workable law should surely be based, but that's another story entirely - necessary, why should anyone else?
The de facto definition of transphobia is that it's whatever a trans person says it is. And the law agrees. The law agrees that if A N Other transactivist perceives a post on Mumsnet to be transphobic, then it is transphobic.
If only the law also included sexism or misogyny as a hate crime, we could just play hate crime poker and raise each other's shouts of TRANSPHOBIA! with MISOGYNY! until we'd broken each other's banks.
The whole debate has been overtaken by the social constructionist idea that individual perception trumps objective reality. And so it's all entirely pointless. Transphobia, as a term, means everything and nothing. Because we are so far through the looking glass that objective definitions of anything no longer exist.