Americans clearly participate in childish behavior. Just demonstrating outside embassies is not one of them. There is no reason to demonstrate at the Egyptian embassy. The Egyptian government defended our embassy. It would make no sense to demonstrate against disorganized Egyptian groups.
Egyptians believe that the offensive trailer that is still being shown on YouTube is sanctioned by the US government, since no one in Egypt, including the Turks and the Brits that once ruled Egypt, would never have permitted such a thing.
There is a difference between an intellectual debate over the merits of Judaism, Christianity and Islam and a piece such as this, which is clearly designed to be deliberately offensive to Muslims in the most sophomoric way possible.
It is similar to the images of the Virgin Mary in elephant dung and "P!ss Christ" that, as I recall, the ratbag right wanted to eject from the exhibitions.
I am personally all for anyone being able to publish anything. But I can see how the Egyptians could be offended.
I recall that rather a lot of Americans demonstrated against apartheid in South Africa in NY and DC. But probably the demonstrations against institutions investing in the RSA were a lot more effective.