There is a lot of opinions obviously. After studying the dance academically for a few years my thoughts on the subject are:
Originally Posted by DancingArabian
Bellydance is a group of dances from and inspired by a style of dance from North Africa, the Middle East, and Near East (Turkey especially) to a specific type of music (movement follows the music). In Turkey it is called Dans Oriental and in Egypt Raqs Sharqi. When speaking of the Cabaret styles (plural) another name I use is Oriental Dance (the translation of the Turkish name). I consider Tribal to still be bellydance (not everyone does) because I can recognize the movement and the music though in the case of Tribal Fusion the music isn't always there. Once the movement changes enough that I can't recognize it as Oriental anymore then I consider it World Fusion instead of Tribal Fusion.
Because they're popular and simultaneously not well enough known for them to be widely debunked. I remember growing up and taking martial arts classes. Some of the wishtory I heard back then would be considered laughable now but then martial arts has become sufficiently widespread that people now aren't so likely to believe them.
When they become sufficiently divorced from Oriental Dance, absolutely. Mainly though I just call it "what was that?"
Define accurate? There are many different styles of bellydance. Some have more latitude then others. Just get the name right and I won't care. Call a Tribal Fusion performance Raqs Sharqi and I will wonder what you think you're doing. If you are doing some type of Fantasy Fusion then just say so.
The costumes for the different styles is not just an aesthetic choice they amplify and emphasis the movements. While still recognizable as bellydance there are differences in interpretation and how those movements are used. There is a reason that Egyptian style dancers trend toward sleek costumes that allow for miniscule small movements, that Turkish or American style dancers wear fringe or coins and draped fabric that will emphasize and amplify stronger hip and chest movements, that ATS dancers fluff up their hips with layers of ruffles, and so on and so forth. Wear something that doesn't fit the style and not only will you have people confused you will miss out on showing your skills properly.
The first step is not trying to "perform, market, and costume" yourself to the public until you actually know how you are supposed to "perform, market, and costume" for your style. Study it, the history of it, and the dancers who came before you and you should be just fine.