Interesting BBC piece on a draft Egyptian constitution. The devil is in the details and in how it's going to be lived out.
A nod to sharia is in there, but it was in the old one as well. Before you get too hot and bothered, there are umpteen takes on sharia; in context, it would be the Muslim analog of "Biblical principles", which depends on who's doing the interpreting.
The lead interpreter is slated to be Egypt's oldest college, al-Azhar University. It is supposed to be consulted on how things mesh with sharia; you could read that to make al-Azhar like the Congressional Budget Office and have it "score" a bill, but not take any recommendations of the CBO to heart...
...or, al-Azhar becomes a sharia Supreme Court, getting veto power over legislation. The latter would likely be a two-edged sword, since it seems more conservative than liberals would like but not as conservative as some Salafi would like. Depending on whether the ruling folks at al-Azhar are stacked in favor of the Brotherhood, it could serve as a moderating influence or justification of taking a more harsh line.
Christians do have a "People of the Book" status as a semi-protected religion in Islamic lore going back to Mohammad, but how much wiggle-room Chrisitans have depends on the graciousness of the Muslims in charge. That will be one of the bigger headaches heading forward; being devout enough to keep Abdul Doe happy, but tolerant enough to keep the west happy.