I have been belly dancing since I was a kid, and I have just recently started burlesque. I have received a lot of criticism for combining the two styles. Where I live, Adelaide, in South Australia, it is very conservative and quiet. The burlesque scene has only just really started up, and while belly dancing has been in Adelaide for a really long time, there is still a lot of negativity. I brought over a dancer from Melbourne to perform Belly dance Burlesque, and some students from another school in Adelaide left part way through the show because they were so offended (she didn't even show any skin!!!)
I must admit, I feel a little uneasy about dancers who combine belly dance and burlesque but don't really qualify what the two styles are or how they differ. I completely understand reservations about hybridity. Belly dancing is sensual yes, but (at least I believe) that it is more about interpreting the music, dancing from the soul and sharing it with an audience. I don't think it is all about sex or sensuality. I love combining the two dance styles, and there are great performers that have. But I think people need to be really aware that it is not in any way traditional and should be viewed in a completely different light.
I think it is the same situation with tribal and fusion belly dance. When these styles started first emerging, there was a lot of criticism, and now fusion has taken over the world!