Full on coating, a PITA, warrants some kind of scorched earth stripping, stripper, drain cleaner, etc. Fast, effective, nasty.

Anodized can often be sanded some with a sanding sponge that will conform to the shape better, and then scrubbed with Scotchbrite and maybe rust/corrosion/cleaner.

I can usually get an acceptable happy medium. The trick is to stop before you make a too nice spot and have to keep going.

Elbow grease is quickly becoming harder to come by.