The struggle in Egypt
Yes, the Muslim Brotherhood won the election last year. Winning an election does not mean that every action a party subsequently takes becomes legitimate. This is why most democratic countries have constitutions which limit the powers of those who win office. Hitler won power in an election; the US has a major party largely dominated by theocrats which could very plausibly bring them to power someday.
Islamists have a built-in advantage in Muslim countries newly freed from dictatorship. Like dictators everywhere, dictators in Muslim countries murder and suppress their enemies. But they're often reluctant to come down too hard on Islamists who are, to put it bluntly, scarier than secular liberals. So when the dictator finally falls, the Islamists are the only united and organized force left standing, and can take power (by election or otherwise) before secular forces have time to make themselves competitive. That happened in Tunisia after the revolution there, and seems to be happening in Libya; it happened in Iran in 1979, and is on course to happen in Syria if Asad falls. And it happened in Egypt.
Despite this built-in advantage, the Brotherhood won only 25% of the vote in the first round of voting and 51.7% in the runoff. Turnout in both cases was low even by American standards. There were allegations of ballot-rigging, and of vote suppression aimed at the Christian minority, which strongly opposes the Brotherhood. Once in office President Morsi issued edicts giving himself sweeping powers, while moves toward Islamization of the state aroused widespread opposition. The Brotherhood proved unable to manage the country, and crime and unemployment exploded. As protests against its rule mounted, the Brotherhood resorted to ugly tactics.
Since the military coup, the Islamists have unleashed an onslaught of violence against the Christian minority. As best we can tell, Egyptian public opinion supports the military. Many are baffled that the US seems to sympathize with the Brotherhood and to want to push the country back into the morass from which it just escaped.
The Brotherhood militants whom the military has been shooting are marching in the spirit of Rushdoony and Khomeini. If the same situation were happening in the United States, I know which side I'd be on.
A reminder of what secular Egyptians are up against:
More on the attacks on the Christian minority: