I've been on a dating website for several years now, both before and after I openly came out about my crossdressing. In that time I have experimented with both having and not having it mentioned on the site. I have now committed to having it on there because I do it too often and it is too much a part of my daily life that to not would be dishonest I feel. But to be honest I can't say that I have discovered a significant difference in the amount of responses that I do get from girls I will message on there when I do or don't list it. And, I can definitely say I've had much more success in parlaying the responses that I do get into an actual date, and never in the dating situation has my clothing been the issue of why or why we don't continue.
Now, consistently the girls have joked that their biggest hesitation with me was being worried I'd look better than them in a skirt, though I always feel this is a joke and doesn't actually lend credence to the "competition" argument.. And one girl, my ex-girlfriend that I broke up with when I moved from Ohio to California, did tell me she needed to go slow with me dressing with her in public, because she was really skittish about being the focus of attention. I think this one is a pretty real concern. Like it or not, we attract eyes and whispers and not a lot of people are okay with that. But what ended up happening is she randomly called me one day when I was out, she found out I was nearby where she was and asked if she could join me, and I had to warn her, yes but I'm wearing a skirt. She said she wanted to see me anyway and she came, and once she saw it was really no big deal, she was fine with it from then on. The point being that if you can be patient and sensitive to her concerns and her speed and comfort levels, it can really help with the acceptance.