Can I search for Etched Champion with Enlightened Tutor?
Yes, it can; for no less than three reasons:


Enlightened Tutor (like all other 'search your library' cards printed so far) does not target a specific card in your library, so protection doesn't play a role here.
Protection from X only functions when a permanent is on the battlefield. (Though players can have protection from X as well.)
Etched Champion's Metalcraft ability only works while it's on the battlefield, so it doesn't have protection to begin with.


(not 100% sure about the third one, actually)