You can, of course, use just about any camera to shoot theatre photography. What’s the point of forking out extra pounds for ‘better’ kit? I’d argue that there are several compelling reasons – quality, versatility, extensibility.
I use a Nikon D700 – a DSLR with an FX or full frame sensor. So what? Simple: it delivers superb quality in low light, with very little noise at very high (6400+) ISO values. As you move down the scale of sensor size, then typically noise increases with pixel density and maximum useable ISO is lower. Your options for low light photography reduce proportionately and the result is a lower quality image captured at the sensor. (If you’re not too sure about any of these terms then pop them into your favourite search engine.)
For me the piece of glass on the front of the camera is easily as important as the body. Probably more so. A high quality professional lens will last a very long time and will most likely remain compatible as you progress through the manufacturer’s range of bodies. I still use Nikkor lenses that I bought in the 1980s. They may be manual focus but they deliver full open aperture-priority metering on the D700. Professional lenses are more robust and usually faster, i.e. have a wider maximum aperture. This means capturing more light, which is important not only for exposure but also for focusing on a darkling stage. So you will infer that slower lenses will be slightly more restrictive in scope and ease of use in the gloom. Succinctly put then, fast glass is good for theatre work.
If you’d considered getting a flash then you can save money. You don’t need one and shouldn’t use one for stage work. Respect for the subtleties of the lighting director’s art go straight down the toilet if you’re splatting white light from a tiny reflector all over the scene. Flash, on the other hand, is a sure way to earn the undying affection of the actors…
Sometimes even with fast glass, an FX sensor and high ISO you still can’t achieve an adequately quick shutter speed. In these cases I use a monopod – a reasonably portable, unobtrusive support that allows you to get away with slower shutter speeds than those achievable hand-held. Remember, though, that while things aren’t moving around at your end, actors on stage will be, and will require a minimum shutter speed to be captured sharply.