Transvestite rhymes with:
hittite, arganbright, argenbright, barite, bauxite, bouknight, buchheit, burright, cortright, couponite, crosswhite, ferrite, gaslight, gesundheit, halite, hebenstreit, hessite, hittite, hypolite, kernite, landviewite, leifheit, ludite, nephrite, perlite, previte, pyrite, raphaelite, searight, semite, stutheit, termite, tracheophyte, weisheit
Transvestite sounds like:
transfixed, transfused, transposed