Skepticism is called for. The prohibition on women going out without a male guardian is not “extremism.” It’s basic, mainstream Sharia: “The husband may forbid his wife to leave the home…because of the hadith related by Bayhaqi that the Prophet…said, ‘It is not permissible for a woman who believes in Allah and the Last Day to allow someone into her husband’s house if he is opposed, or to go out of it if he is averse” (Reliance of the Traveller m10.4).

The Saudis are unlikely to go against a command of Muhammad. This relaxation of the prohibition is likely to be window dressing designed to improve Saudi Arabia’s international image.

“Saudis to Let Women Travel Without Male Permission, Newspaper Says,” by Vivian Nereim and Sarah Algethami, Bloomberg, August 1, 2019: