I’m not sure I’d call the whole show transphobic, however I only remember two or three times they mentioned transgender people on the show and it was always in a bad context.

One time Sheldon and Leonard were discussing how Penny was an improvement in almost every way over the previous tenant next door who was a tall muscular black transsexual (that’s the word they used). Another time Howard told a story where he hooked up with someone only to find out that they were a pre-op transsexual, which got him an “Oooohh” of pity from the audience/laugh track.