This is a great topic. I thought I had it tough being a Ballet grandpa. I used to have to shoot basketball or volleyball in those poorly lit gyms and the answer is was always: Bigger, faster lens.
A bigger lens, like a 300 or 400 gives you more distance to work with, and the opportunity for someone to walk in front of a shot, but also allows for a shallower depth-of-field so those ugly backgrounds can be thrown out of focus.
In ballet, when I can get permission to shoot, it's nearly always from the back or a balcony and I have to use a tripod and available light. Here's one of my best:
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