Yes, it is possible for tap water to cause eye infections. It is contact lens wearers who are at risk. There is a microbe common in the environment including in tap water. Called acanthamoeba, it has two forms: the trophozoite and the cyst.
The trophozoiteis is infective. It can change into a cyst and survive long enough to stick to the surface of contact lenses and then infect the eye. There have been cases where eyesight has been severely damaged in this way.