CAIRO — Stepping from the cloud of tear gas in front of the American Embassy here, Khaled Ali repeated the urgent question that he said justified last week’s violent protests at United States outposts around the Muslim world.

“We never insult any prophet — not Moses, not Jesus — so why can’t we demand that Muhammad be respected?” Mr. Ali, a 39-year-old textile worker said, holding up a handwritten sign in English that read “Shut Up America.” “Obama is the president, so he should have to apologize!”

When the protests against an American-made online video mocking the Prophet Muhammad exploded in about 20 countries, the source of the rage was more than just religious sensitivity, political demagogy or resentment of Washington, protesters and their sympathizers here said. It was also a demand that many of them described with the word “freedom,” although in a context very different from the term’s use in the individualistic West: the right of a community, whether Muslim, Christian or Jewish, to be free from grave insult to its identity and values.

That demand, in turn, was swept up in the colliding crosscurrents of regional politics. From one side came the gale of anger at America’s decade-old war against terrorism, which in the eyes of many Muslims in the region often looks like a war against them. And from the other, the new winds blowing through the region in the aftermath of the Arab Spring, which to many here means most of all a right to demand respect for the popular will.