No, it's not true.
Tranny is the term to be avoided, as it is considered an insult or derogatory to non transvestites, much like the "N" word is considered an insult or derogatory.
Crossdresser became the term to be used instead of Transvestite due to Virginia Prince and the founding of Tri-ess back in the 1970's, which was restricted to heterosexual male crossdressers. The term Transvestite has not used because of the link to being gay.
