Is it considered that trousers become impure—a moral impurity—and is there a fear for the wearer, after washing them, of falling into polytheism, if they touch shoes that stepped on a place where an idol placed in the house was destroyed?

You were right in breaking the statue, because the Prophet, peace and blessings be upon him, said: "Do not leave an image without obliterating it." The statue is not impure just because it is a statue, so the prayer rug, shoes, or trousers do not become impure because of it. The spiritual impurity of the statue does not imply the rulings of physical impurity.