A non-protein fiber is not really dyed but rather stained with food coloring/koolaid. So not only will it be more pale, it will also fade considerably over time. This site explains that:
I have tried a variety of techniques and found the one on knitty.com to work the best (boil the water, remove from heat and add color, add fiber, let cool COMPLETELY). The hardest part is not rushing the cooling, even if you carefully cool the water in stages while rinsing you will still rinse out a lot of color (this is good if you accidently make something too dark). I set mine near my kitchen window and it cools a lot faster but still preserves the color. I've used food coloring from the grocery store, kool aid, generic kool aid and Wilson's dyes (used for cake decorating and found in craft stores-and WalMart, weirdly enough though they don't have much color selection). If you use food coloring you should use vinegar in the water you presoak with, if you use koolaid you don't need vinegar. Kool aid makes the best red, IMO. Food coloring makes a great blue. That is about all I know. I am still unhappy with brown, my yarn just didn't want anything to do with the green tones in the brown so it came out kind of orange rather than brown. It was disappointing.