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.

Not sure about the transphobia, but it is definitely on the sexist side. The whole premise starts out with dumb hot girl being hounded by smart inept nerd and friends. This of course continues in various ways and lets not forget Howard.

I do wonder though, this was pretty much the point of the comedy. Shining a light on stuff like that.

Most older shows don't perform well with more current ideals in mind. Media should be viewed in the context of its time and people were generally less aware of how harmful certain portrayals could be.