The only way to get Islamists out is to fight them, and hard. They aren’t going to vote themselves out. Any other “people of the book” they allow into their government are dhimmis or collaborators. I know liberals just don’t understand that, but that’s a lesson from history. None of the people who ousted Morsi and hold power now are in any way a Mubarak or an Atatürk, and may be worse than the openly Islamist types.
The Islamists are already out. The Egyptian Army is in control, and the Army is dead-set against the Muslim Brotherhood.
For that matter, Qatar just closed the MB’s offices there, too. No fighting!
The MB is losing against Assad in Syria, as well. Fighting!