The main character drinks apple-tinis and is constantly called a girl's name. He's open about his love for his best friend, and refers to himself as a "sensey".
I've re-watched that show more times than I care to admit. There might be a few jokes that didn't age well, but I don't recall anything transphobic.
TOS being from the 60s is harder to rewatch, let alone watch for the first time 60 years later.