One mosque in Dubai lets anyone walk in. That is the entire point of it.

Jumeirah Mosque opened in 1979 in Fatimid style — a gift from one ruler of Dubai to his son.
Six days a week it runs guided visits for non-Muslims under a programme called Open Doors, Open Minds.
Coffee and dates first. Then questions, including the difficult ones.

The most photographed building on that road is also the one that answers back.