This is an uneducated opinion - I think that a fabric that is exposed to any lights over a long period of time will fade. Having said that, about the only time most of my fabrics are exposed to light is when I am cutting, piecing or quilting them.
Florescent lights have mercury, which is toxic to humans, in them. That is one of the reason that they have to be handled so gingerly when transporting them or changing them.
LED lights, on the other hand, can be disposed of like an incandescent light because they contain no harmful chemicals.