My parents (mainly my mom) have more of a problem with my "addiction" to my "silly little cartoons" than they do with whether or not I am dressing up as a boy or a girl when I attend a convention. My parents are divorced and I would visit my mom every summer, there would be a convention usually in the month I was seeing her and she would always ask if I was "going to that silly little cartoon show" or not. It never occurred to her, homophobic as she is, to question the gender of the character I was dressing up as. She just thought it was silly I was dressing up and traveling to the convention grounds on public transit in the first place.
When it comes to my dad, he's always been more laid back and supportive, about my "addiction" and dressing up. Actually my dad is the one who is my photographer really - he's always wanted to be a professional, and so he actually loves it when I dress up (male or female) because he gets to exercise his photography skills. We wind up making a great team that way ^^;
So I guess if my parents have ever been saying to themselves, "oh dear god, our daughter is dressing up as a man, let's worry about her sexuality!" they've certainly never voiced it to me. Mostly they've been as supportive as I can expect them to be, and I'm cool with that.
"It's amazing what a performer will do when the camera is rolling... it's probably a psychiatric illness!"