I want to take photos of a theater scene. I usually use a UV filter for nature photography, but what about a theater scene in a saloon with a dark environment? Is there any specific filter for these situations? Or is it accepted wisdom to use a filter at all?
If you have to use anything then I would suggest a lens hood.
The only reason for that is because of the stage lights coming down and might bounce to cause a flare.
Stages, with lighting, are designed to give a certain atmosphere for the performance so any additional changes defeat the purpose of that lighting.
Now, depending on your location, you may need to reduce color intensity; however, I think most people would do that in post processing. Otherwise, a neutral density (ND) filter might help depending on your situation.
Coming from a film background: you don't need the UV filter in a theater. Yes the lights emit UV, but...you don't need to worry about it unless the "theater" is actually a tanning bed.
UV filters are generally considered to just be lens protectors, because photo camera sensors usually have UV (and infrared) filters directly on their sensors. There is a drawback to adding any additional glass elements to the lens: ideally they don't introduce any distortion or reflect any visible light; in reality they do. In darker conditions you don't want to be adding a filter because you want to maximize light through the lens system. The only reason to keep the UV filter on is if there's a risk of damage to the front lens element because of the shooting conditions.
Theatrical photography is one of the settings most prone to ghosting and other types of flare being caused by a flat filter on the front of the lens. You have a few areas of intense light and a lot of dark areas around them. What happens under more typical bright scenes is that the flare produced by the filter is masked by the brightness of the scene. Not so with theatrical shooting.
Although this was taken in front of a theater instead of inside it, the concept is the same. The bright lights on the upper left are reflected reversed and upside down on the lower right. This is an extreme example, but multiple coatings can only do so much to reduce flare when a scene has this much dynamic range.
The best solution when shooitng in such an environment is to use no filter at all. Instead, use a lens hood to block stray off axis light from causing flare and to also provide physical protection for the front of your lens.