Whenever there is a discussion about how fish react, one needs to consider how two main factors affect behavior. The first is biology. By that I mean the DNA, and the anatomic structure of the fish. In the case of the color red, can fish see red? Yes they can.
The second is population dynamics, how the population as a whole reacts vs a single fish. All the fish in a population do not react identically and yet most discussions assume that they do. Populations behavior is distributed around a mean and the behaviors tapers off in both directions around that mean. A symmetric distribution around the mean is called a bell curve.
So what I am saying is that even if a fish can see red, not all fish will react the same or even have a reaction. So how the fish that sees your red line will react is as much a factor of where it is on the bell curve as to whether it can actually see the line.
When someone says I use red tippet and catch fish so it doesn't bother the fish, what he is actually saying is that red did not bother THAT fish. He cannot assume it doesn't both other fish or even most fish.
In the case of the color red and water, other factors of water depth, clarity, and color affect visibility. Go HERE
to see how water affects color. As has been said before, red is the first color to disappear and when there is no red light, red line will look shades of grey to black depending on the how red the line is.
The differential absorption of different wave lengths (color) in water means that red light soon disappears. In shallow water, red can be seen but at 1 meter or 40 inches, the color red in the ocean is pretty much a grey or a grayish red.
My view is that although fish have a lateral line, a fishing line does not cause a detectible change in underwater vibrations. The lateral line detects longer wavelength or low frequency vibrations from a struggling fish or a swimming fish and not high frequency vibrations.
More than color, I am concerned with
1. The surface reflectivity of the line - does it throw off bright reflections or is the surface dull. Reflections increase detectability.
2. Light refraction/absorption - is the the light distorted as it passes the line or does the line absorb all or some of the light?
3. Suppleness - does the line bend easily so as to conform itself to differences in water flow. This ability reduces drag.
4. Stretch - how much does the line stretch. This affects strike detection and reaction time.
5. Does the line absorb water - this affects diameter and strength. Nylon mono absorbs up to 30% water by weight and gets weaker. Fluorocarbon does not.
6. Abrasion resistance - maintains strength
7. Knot holding
As for color, I prefer clear lines. Clear lines most of the time blend in best with the water they are in. I believe they are universally less visible than colored lines for most circumstances.
Even in dirty water, you can see the water color transmitted through the line. Think of tippet as plates of window glass rather than a line. Imagine narrow strips of colored glass in different types of water. Only the clear glass (tippet) adds nothing and attenuates the least amount of light from the other side of the glass (tippet).
How about when it is floating and seen against a blue sky? What tippet color is least visible? But more than that, what tippet color casts the least visible shadow against the river bottom? The answer is clear.