What a great read, going through this thread. I probably can't add a new point, but can offer my perspective.
I think the gay/trans position is becoming more and more accepted due to the media and other events that have brought it to the forefront. The leading reasoning for this (paraphrasing here because I don't have any actual study or data to back this up) is the argument that it is "innate" or they were "born" with it. It is described much more eloquently, but you get the point.
Crossdressing, is therefore classified as a choice. It's my choice to wear clothing that is classified as "women's clothing". I believe that if there is a bias against cross-dressing it is because it is viewed as a choice, and in the narrow minds, that means there is also a choice "not to" cross-dress.
I never made the link to sexual preference and cross-dressing, although now that I think about it, there might be a bias there.
Sorry there is nothing earth-shattering with my perception, but thought I would add it nonetheless.