PhotosGuy is basically correct.
To the extent that the lighting is designed, you want to reflect that in the image. Generally, setting your camera for tungsten is the best you can do.
The modern trend is toward LED lighting. It's not hard to see why--runs cooler, cheaper, and a lot longer between bulb changes 'way up high.
But stage LEDs absolutely stink for photography and video, and they're nothing much you can do about it.
Stage LED lights, if you look at them, simulate "white" light for the eye by merely having a sprinkling of separate red, green, and blue LEDs on the light panel. That fools the eye well enough, but not the imaging sensor.
And most of the time (in my experience), only the main lights have even all three colors of LEDs. Most of the auxiliary lighting will be just red and blue LEDs.
Or, lordy, they'll just mix in everything. Maybe the spots will be tungsten and all the auxiliary lighting some mixture of RGB LEDs and RB LEDs.
So, if there are some tungsten's in the mix, you can do a bit of tweaking in post. but you'll largely have to live with a magenta cast otherwise, because the hues you need just don't exist in the light you have to work with.