If the Egyptians want to ban beer, segregate beaches, and require women to wear modest clothing in public--let them. Democracy is a good thing. They absolutely will not do with their democracy what we would do with ours. They might even do a few things that later on they will regret--name a democracy that hasn't. Please don't tell me that as we grew up as nations Canada and the United States always managed to extend full human rights to everybody. We failed. They will fail. We grew up, and so eventually will they.
The important thing is to reinforce their commitment to democracy, whatever it is the choose to do with it. Certainly we can criticize the shitty things they may sometimes do, but that's secondary. We have to support their democracy in a primary way.
Externally, that may mean they go around and antagonize Israel for awhile. They may even go around antagonizing us for awhile. Thing is, their leaders really will represent the Arab people, and any conversation with them will be an honest conversation about the actual issues Arab people care about. No doubt they care about stuff we'd rather they didn't care about, but that's life. All Middle Eastern policy up until now has involved "smoothing over" the concerns of Arab peoples--offering them money, deals, status in exchange for shutting them up. We never really did deal with their issues. We only ever bought off their illegitimate leaders.
I'm pretty sure that honest conversation will be a difficult one, that it won't go smoothly, that they'll demand a bunch of stuff we won't want to give them, and that it'll go back and forth for maybe even 20 years while we try and talk sense to them and they try and talk sense to us. At the end of that process, though, whatever it is, should be a REAL understanding, and a peace based on mutual respect, and everybody actually having their central issues addressed.