Protection from a color means that the target creature can't be blocked by creatures of that color, can't be the target of spells of that color or abilities from sources of that color, can't be enchanted or equipped by Auras or Equipment of that color, and all damage that sources of that color would deal to it is prevented. Nothing other than these events is prevented or illegal.

Similarly, protection from colorless means that the target creature can't be blocked by colorless creatures, can't be the target of colorless spells or abilities of colorless sources, can't be enchanted or equipped by colorless Auras or Equipment, and all damage that colorless sources would deal to it is prevented.

A permanent gaining protection may cause a spell or ability on the stack to have an illegal target. As a spell or ability tries to resolve, if all its targets are illegal, that spell or ability doesn't resolve. None of its effects happen, including effects unrelated to the target. If at least one target is still legal, the spell or ability does as much as it can to the remaining legal targets, and its other effects still happen.