This is a kind of addendum to the post I wrote about theatre photography, but it's something I've only just got round to doing successfully after working out the theory. If you're photographing a show with projections, try to choose a shutter speed that's a multiple of 30. 1/60 is often too slow for a moving subject, but I managed to use it sometimes and got a nicely colour balanced projection. However I mostly shot at 1/125 and it's easily close enough with a small amount of correction in post. Any higher is tough in low light, and the projector itself is often not bright enough to pick up, defeating the whole point.
I don't know exactly why this works, but I had read about something similar when shooting a scene including old TVs. The effect of shooting at 1/200 for example is to separate the rgb colour channels so in each shot the projector has predominantly one of those brighter than the other two. If you end up with this, the green is generally easiest to fix with a selective hue adjustment in photoshop, but obviously this only works with monochrome projections.