This is a subject that will probably run and run, there's so many different theories and opinions.
One line of thought is that the more visible the line is the less likely the fish are to spook as they're not surprised by touching it, another is to try and make it as inconspicuous as possible, clear, camo, back leads etc.
I have seen red line advertised as being invisible to fish and also to arouse their curiosity and lead them to the bait. Debate away, when we find a talking fish we'll have the answer.
Something to ponder though, last year I got a new head torch with a red setting, the theory being that it doesn't destroy your night vision (very true) and that fish can't see red light.
On a sea Trout visit last year I went with the keeper to have a look at a lie which had held a couple of Salmon the previous evening, it was dark at this point but there was some orange light from street lighting. There was a fish in residence and wanting to try and see exactly what it was I tried an experiment. Using the red setting we had a good look, the fish remained undisturbed and proved to be a sea Trout about 2lb, sea Trout are just about the spookiest fish I know of so this was proof to me that the red light certainly didn't disturb it, it just stayed where it was.
Switching to the normal light setting, the second the fish saw the light it vanished in the blink of an eye.
Food for thought.