You can neutralize the strong magenta influence typical of LED stage lighting by setting the white balance setting in the camera for most DSLRs. Canon calls this feature White balance correction. It can be accessed under WB Shift / Bkt menu item in Canon cameras. Most other camera manufacturers have similar settings.
You may also need to adjust the exposure to compensate for a much more powerful color channel than the others. A combined histogram (and the automatic exposure of your camera) that averages the three color channels will not show the totally destroyed channel. When viewing images, set your camera to display separate red, green, and blue histograms on the LCD monitor and adjust the exposure according to the most intense color.
From pages 172 to 73 of the EOS 7D Mark II Instruction Manual. Other EOS cameras are similar.
Move the cursor in the opposite direction to the colors on the four borders of the graph that dominate your images. If you exit the WB correction screen without pressing the key Together button first, your changes will be do not be applied!
You can use WB correction to produce a single image or WB bracketing to produce three images with the WB correction placed in square brackets along the magenta outline.<--->green axis or blue<--->amber axis.
Note that when using WB bracketing, three images are recorded for each shutter action with the different WB corrections applied. This means that the write time on your memory card for each shutter operation is the same as for three different images. This means that when using WB bracketing, your burst maximum before the camera buffer is full and your frame rate reduced by about 1/3 as many shots only when you do not use WB bracketing.
When shooting under LED stage lighting that gives the typical pink appearance of the examples of the question, I usually use a WB correction of about 8 or 9 steps to green and about 2 steps towards blue (G9, B2). Each step with the Canon EOS cameras is roughly equivalent to a 5 mired color conversion filter. I usually adjust the color temperature manually by trial and error. At the bar, I shoot most often with 3700-4200K and a correction of about WB (G9, B2).
You will just need to use it in each location and see how the lights are set for each performance in the same place. If the lights alternate with colors, I do not try to delete them completely. I simply set a median value when the three LED colors (R, G and B) are lit, then the variations remain throughout the performance. When only one color LED is lit, you are almost limited to a monochrome image, whether with the color used or in black and white. Even if the red / magenta and blue lights are lit, if there is absolutely no green, the battle will be tough, because the Bayer hidden digital cameras are twice as sensitive to green light in the middle of the visible spectrum as red. and blue at each end.
If you shoot in RAW format, all camera settings related to color temperature and WB correction may be changed later. If you shoot in jpeg format, they are more closely related to shooting. With jpeg files you can adjust the R, G and B curves independently. A good HSL tool can help remove the color cast from jpeg files, but radical changes will not be very good. Saving raw data gives you a lot more latitude for color correction in post. If you do not use the raw conversion software of your camera (Professional Digital Photo 4 Canon), your WB corrections may not be applied automatically when you open the raw file on your computer.
One of the main advantages of shooting raw images over jpegs is the ability to use the color picker in the raw conversion process. Another advantage is to correct beyond the limits of the White balance correction tool. If I have dialed the maximum +9 for green in the device and I want even more green, I can do it in a raw editor. If you can approach enough of a white object under the lighting of the stage to take a picture that can be used appropriately to set a Custom white balance then you can do pretty much the same thing in camera. But you do not always have such an opportunity to capture a white object under the light of the stage with enough size to use as a camera. CWB. With the post color selector, you can use a much smaller area of the total image to set the color temperature / WB.
Even with your highly compressed JPEG image, I used the white balance tool at click, and then adjusted the hue, contrast, and saturation levels. I then used an HSL tool to reduce magenta, yellow and green saturation while slightly increasing the green and yellow luminance and lowering the magenta luminance (the singer's skin was blown into the magenta channel). Here is what I got in a few minutes:
Here are two versions of the same picture that I took several years ago. The first is what an integrated jpeg would have looked like using "Auto WB" and Canon's "Portrait" image style. The only difference in the second was the use of the "Click White Balance" pipette to adjust the color temperature and the white balance correction to the raw data in one click. (The tools I'm using now are a little more refined, but just the "white balance per click" brings it very fast!)
For more information, see the following questions:
Blue / red light off making pictures blurry
How could I neutralize purple lighting?
What are the appropriate lenses for concert photography?
I can not get crisp pictures when I shoot a concert from a press space
Best lens and camera settings for a dance concert with medium lighting
Why do RAW images look worse than JPEGs in editing programs?