You are facing a low CRI index.
CRI is the Color Rendering Index, and this means, effectively that you do not have enough light across the spectrum.
Some lights emit only portions of it, and our brains adjust the color to what they think the color should be, but as a mechanical/electronic device, a camera is more limited to what actually is receiving.
Look for higher CRI lights. The scale limit is 100, meaning that the light emission spectrum would be the same as the daylight. So the closer to this number the better color you will get. For practical purposes, a CRI above 85-90 could be decent enough. One above 95 can be considered a "Pro-level"
If you search a store, a lot of led lights mention the CRI value, use those terms on a search, for example on the Amazonian river store "LED LIGHT CRI".
lights is not uniform across the spectrum?
The spectrum does not need to be uniform, it just needs to be "uniform" enough compared to daylight spectrum (which is not uniform at all)
It looks almost colorless when I reduce the red component
You need to differentiate the CRI to the color temperature. You need additionally to check two factors.
The color temperature of the Light (Warm, cold)
And if you are setting your white balance correctly on camera.
It also could be corrected to some degree using a custom color profile or using some "pro-grading" program. Give Davinci Resolve a Try.