Is the impurity of a non-Muslim who does not cleanse himself after urinating, nor wash the site of impurity or his hands after relieving himself, and this impurity transfers to shared utensils and through handshakes, considered an unavoidable impurity?

The hand does not become impure by shaking hands with someone whose hand's impurity you are not certain of, or if you are certain of its impurity but both hands are dry. However, if you are certain of the impurity of the hand of the person you shook hands with and one of the hands was wet, then your hand has become impure. Similarly, the hand does not become impure by touching an object that was touched by someone whose hand's impurity you are not certain of, or if you are certain of its impurity but both the object and the hand were dry. However, if you are certain of the impurity of the hand of the toucher and either the object or the hand was wet, then your hand has become impure.