Why do color channels from a digital camera respond slightly to lights of other colors?
Because the filters placed in front of the silicon on a Bayer masked filter all allow some of all the wavelengths of visible light to pass through. They just allow more of the light at wavelengths near the color of each filter to pass.
Back in the days of B&W film photography color filters were often used. At first glance that might sound a bit ridiculous. But what color filters allow one to do with B&W photography is separate the similar brightness of two objects of different colors. If one has a red flower and a green flower in a scene and both are the same brightness, then an unfiltered B&W photo would show both as the same shade of gray. If one places a red filter in front of the camera, more of the light from the red flower is allowed to pass through the filter than the light from the green flower. Now the red flower will be a brighter shade of gray than the green one will in our photo. But we can still see details in the green flower, they're just darker than they were before. Everything that isn't the same exact shade of red as the filter does not become pure black in our photo. The red filter has not eliminated all green light, it has just reduced green light compared to red light of the same intensity.
"Everything that isn't the same exact shade of red as the filter does
not become pure black in our photo."
Yet that is what it seems many people expect of the Bayer masks on digital image sensors - they seem to think that only a range of green wavelengths make it through the green filter, and only a range of red wavelengths make it through the red filter, and only a range of blue wavelengths make it through the blue filter.
The color filter arrays on Bayer masked imaging sensors work exactly the same way as color filters do with B&W photography. Each sensel (a/k/a pixel well) in an imaging sensor records a single brightness value. All light that passed through the filter above it is recorded equally, regardless of the wavelength of that light¹. The color filters of a Bayer sensor are also working similarly to the way the cones in our retinas work. That's why a Bayer masked sensor and an RGB display device can recreate colors that look "correct" to our eyes. They're using the same three channels that our eye/brain system does to create the colors we perceive.
¹ Technically speaking, the response will vary by the silicon wafer's response to various wavelengths of light when there is no color mask in front of it. But the response to a 'blue' photon that passes through the bayer filter will have the exact same effect on a red, green, or blue filtered sensel. It's just that fewer 'blue' photons that strike the front of the Bayer mask will get through the red and green filters than get through the blue one.