RIYADH—Saudi Arabia's king replaced the hard-line chief of the country's morality police with a more liberal cleric who has encouraged greater women's rights, a change welcomed by activists as a sign that the monarchy would continue to pursue cautious social reforms in the face of political upheaval in the Middle East.

Saudi King Abdullah bin Abdulaziz al Saud on Friday appointed Sheik Abdulatif al-Sheikh to oversee the religious police, who roam the kingdom's shopping malls and streets enforcing a rigorous version of Islamic...