Do wet clothes—which have been wrung out in the washing machine—become impure when they fall onto the floor of a room that has been stepped on by a wet shoe with which one entered the bathroom, knowing that I suffer from Waswasah (obsessive doubts) and prefer to follow the easiest madhhabs?

The default state of a bathroom floor is purity unless one is certain that it has been contaminated by impurity. Therefore, shoes, the room, and clothes that fall on its floor are not rendered impure merely due to doubt. If a specific spot becomes impure and dry clothes fall on it, the impurity does not transfer. If either the clothes or the spot is wet or damp, there is a difference of opinion regarding the transfer of impurity, and it is permissible to adopt the view that it does not transfer in this case. One should disregard this matter and not dwell on it.