Is the background behind this Balinese dancer too busy? In many ways it is, definitely. There is a lot going on in terms of color, form, and texture, and it draws attention away from the dancer. But Balinese temples are an integral part of dance on this very spiritual island, and therefore the background helps tell a story. The dancer would look great against a black background, but that would be a different kind of picture. This shot helps to illustrate the culture and religion, and in my opinion, then, the background works.
In essence, there are two subjects here – the dancer and the background – and as such they are both important. Other photographers can disagree with my assessment, but this is how I see it.