RIYADH, Saudi Arabia — Nader al-Mutairi stiffened his shoulders, clenched his fists and said, “Let’s do our mission.” Then the young man stepped into the cool, empty lobby of a dental clinic, intent on getting the phone number of one of the young women working as a receptionist.

Asking a woman for her number can cause a young man anxiety anywhere. But in Saudi Arabia, getting caught with an unrelated woman can mean arrest, a possible flogging and dishonor, the worst penalty of all in a society where preserving a family’s reputation depends on faithful adherence to a strict code of separation between the sexes.