Is inserting one's hand to clean the anus after defecating considered permissible or forbidden?

As long as you are cleaning the outer part of the anal opening, there is no harm in that, whether it is with fingers or with the edge of the hand. The important thing is not to be overly meticulous or exhaustive in reaching the inner part of the private area, for Al-Ghazali said: "And one should not be exhaustive in it by exposing the inner part, for that is a source of obsessive doubts." Everything that water does not reach is considered inner, and inner impurities are not subject to the ruling of impurity until they emerge. Whatever appears is subject to the ruling of impurity, and its emergence is defined by water reaching it.