It's extreme because we're used to times of peace and comfort. Public executions is totally foreign in our time and the concept of enforcing morality is unheard of outside of Arab countries.

During the Inquisition, it became necessary to publicly execute illegal immigrants that refused to leave Europe after the Reconquista. They were often Moors that squatted in homes during the Muslim occupation and attempted to keep the land after the Muslims were forced out. If they weren't executed then they'd simply keep trying to come back. Also they were all given the option to leave in the first place yet refused.