Do clothes or shoes become impure by a person touching them with a hand that has traces of beer on it, or by touching a box containing beer cans?

Your hand or clothes do not become impure by touching someone's hand, for the default state of things is purity until you are certain of impurity, and incidental doubt does not harm. Similarly, your shoe does not become impure merely by touching a carton containing wine bottles. It is advisable to turn away from these whisperings (waswas) due to their harm to the Muslim in their religious and worldly life.