President Morsi says Egypt will not play by American rules...

Okay.   Just be prepared not to play with American money.  

I have no problem with Egypt being its own sovereign country.  But we should not subsidize positions we disagree with.  Egypt could have a thriving economy.  It could be like the Asian Tigers, or for that matter Dubai and the Emirates, if it chose to do so.  But decades of socialist policies and rampant corruption have stifled any chance Egypt had to prosper.  Israel is a red herring.  The fundamentalists are in power not because of Mubarak being pro Israel (that is a lie because if Mubarak was pro Israel it was only because he did not fight a war with Israel while he was in office)--but because Egypt's economy is a basket case.  If the Muslim Brotherhood does not deliver a better economy to Egyptians, that party will be out of office too.

Mubarak's claim on power was trying to get growth to keep up with the Egyptian population  and keeping the Egyptian Army happy.  If Morsi wants to go on a new path, let him.  But giving him aid is not going to mitigate harm it will be just feeding the problem.  And Obama has to make that absolutely clear that the U.S. will cut off aid (we should have done that with the September 11, 2012 protests).

Egyptians governments using anger against Israel to deflect anger against the regime is an old tactic.  China is doing the exact same thing with Japan, to cover for its economy slowing.  We will never bail out China.  We do live in interesting times.

Update:
I agree that peace is possible in the Middle East, but we are not going to get there with the way Barack Obama has set it up.