If you wanted to get technical, then transgender is an umbrella term that includes drag queens.... and the differintiation that must be made would be between them and transsexuals.
However, yeah - if someone insults someone who is special to you, then it is pretty easy to dislike them, and very understandable. And, well, I also believe that trans people and drag queens should be recognized as different entities - after all, people relating us to drag queens is a significant source of some of the meanness that people put us through at times.