As long as the animal likes attention, I have no problem with it! As long as its safe, of course.
I've dyed my poor cat before^^, he was a wonderful pink color. It was animal-safe, and he loves baths, so I thought I would give it a try on him. He didn't mind it one bit, but he doesn't go out into public, so he didn't get any special attention from it. Its all gone now, though.
Frisk has been lightly dyed green before. He loves public attention, so I knew he wouldn't mind. On walks, he either got people coming up to him petting him and all (ie being his "fans" ) or extremely weird looks.
I would NEVER dye Ethan, though. Just being in public makes him scared, getting too much attention from strangers makes him seem so scared that he looks like he's about to wet himself.