See this article from a Canadian paper, The Globe and Mail, to read a very clear description of how Egypt has arrived at a place where its new Muslim Brotherhood-run government is threatened with revolution anew.
Many in this poor country recognize that acting in ways that drive away foreign tourist income makes no sense. That, and the Suez Canal are essentially Egypt's only sources of foreign exchange, with which to import much of its food.
Also, like Turkey, this largest of Arab countries has a substantial minority, or perhaps a majority, who favor a secular state. Add to that Egypt's indigenous Christians, the Copts, and the numbers become substantial.