While I am a big proponent of being able to play with lots of different music to add variety to your dance, particularly when we perform for mostly bellydance audiences (and who wants to hear Miserlou again), I would think one of the base requirements of being a bellydancer is listening to, appreciating, and dancing to Middle Eastern music. Otherwise, I would think any number of other styles of personal expression would make more sense: modern dancer, interpretive dancer, or world fusion dance is my favorite.
So before I make this sound like I am just judging other people and don't know of what I speak, I myself have also struggled with this topic.
When my first pro troupe was younger and trying hard to establish our own voice, we began venturing in a lot of different directions to seek unique inspiration. Some were closer to bellydance, and some were much further afield. Not just with movement, but the music, too, was getting further and further from bellydance. We were having fun, and we were getting lots of workshops and performance opportunities, and it was a real peak in our troupe history. But the more we became known for our fusions, and our non-bellydance stylizations, the less time and energy we spent on bellydancing. Pretty soon, our music, choreography, movement vocabulary, and costuming had collectively grown so far from bellydance, I had the realization that we weren't really bellydancers any more--at least not primarily.
I still get requests for the workshop and performance material we were doing all those years ago. People really enjoyed it, we had a great time, and as a teacher my workshop income was about twice as good then. It's hard to take that kind of loss as a businesswoman, and so I have a unique understanding of and empathy for other teachers and performers who aren't really bellydancing any more, but continue to get a lot of work and notoriety from the community. But for me, I wanted to bellydance, so I made it my personal focus to study, teach, and perform the music, movement, costuming, and culture which supports that goal.
Just my personal experience, for what it's worth.