The Romans discovered how to use alum as a 'mordant' in dye processes... the hard aluminum salts act like teeth to help dyes stick to slippery fibers. Trouble is, it is abrasive. We used to wash our expensive towing lines with fresh water to remove abrasive salts after using them in seawater. The other problem is that alum is acidic. Combined with chloride it can become more acidic, and can produce hydrochloric acid, which is very strong. Amsteel has excellent chemical resistance as well as abrasion resistance; nonetheless, I wouldn't use an acidic abrasive like alum on it.
I order gray or silver Amsteel and haven't noticed anything on my hands. But then, my hands are usually covered with soot from messing with wood stoves... I should try washing them with alum.
If I don't like the color of my Amsteel - I dye it further
"If you find yourself in a hole, the first thing you should do is STOP DIGGING "
... I bet the fiber is so dense that dye simply will not penetrate deeply...
I know that on a molecular level, dyneema (aka spectra aka UHMWPE) is super smooth and slippery. I am sure that is what prevents the dye from sticking well. It has a specific gravity of about 0.98, floats, and technically is quite un-dense.
Now what keeps it from holding on to itself so well...the world will never know. It's like trying to figure out how many licks it takes to get to the tootsie roll center of a tootsie pop.