Yes, men and women should take their shoes off before entering mosques,
women will be asked to cover their hair, their arms and legs.

Tourists are welcomed in almost all historical mosques in Egypt, expect
when these mosques are being used for prayer, on Friday and during the five
prayers of the day.

Same of the historical mosques. Tourists are welcomed in most of the
historical churches, except during Lent, and the modest dress is also
recommended while visiting churches in Egypt.