Abri

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.

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.

The legality of a spell’s targets is checked only as that spell begins to resolve. If Shelter gives the targeted creature protection from white, you’ll still draw a card.

You can’t choose “artifact” or “colorless” as Shelter asks you to choose a color, since those are not colors.