The anger which the protesters are expressing has been brewing for decades under a Mubarak regime which aligned far more closely with Israel than the Egyptian public. But while the Mubarak regime acted with little regard for the Egyptian public, it's policy was based on security interests, not any love for Israel. As a result, Egyptians have had little contact with Israelis, and Israel has had very little penetration into the Egyptian public sphere. This means that anger and frustration with Israel has been removed from serious consideration of Israel's side of the story.
The reaction in the Israeli and American Jewish community so far is one of fear. A breach of an Israeli embassy is a serious matter which is likely to put even more pressure on an already delicate relationship between the Israeli government and the Egyptian Supreme Council of the Armed Forces (SCAF). Cynics will point to the riots as proof of pervasive anti-Semitism and anti-Israel sentiment in the Arab world.
In the short term, Israel's primary interest is of course to secure its diplomatic personnel and reassure its public that the event does not threaten Israel's borders. In the long term, however, the tactical prescription is clear, and must occur imminently. After the fall of President Mubarak, Israel has no choice but to engage the Egyptian public.
There are a number of Egyptians expressing concern at the chaos happening at the Israeli embassy. They argue the actions are brash and detract from the real purpose of the January 25th revolution. By empowering these moderate elements (signaling in press engagements that Israel doesn't consider violent rioters the majority of the Egyptian public, for example), Israel can help delegitimize future riots and begin building the foundation of a public diplomacy strategy in Egypt which addresses some of the misperceptions Egyptians may have about Israel.
Already, Israel has made significant progress in its engagement with the Arab world. The government's social media presence in Arabic is impressive, and there are two IDF Arabic spokesmen (Avichai Adraee and Ofir Gendelman) who regularly appear on Arabic satellite media. The next step will be to hone not only the language of the message, but the information it conveys. Empathizing with the frustration of the Egyptians and facilitating engagements between Israeli and Egyptian citizens will be key first steps to this effort.
Of course, not all of the protesters and those who oppose Israel are motivated by raw emotion. Some are frustrated over the lack of progress in the Israeli-Palestinian conflict, and many fear Israel's military prowess. In its policy deliberations, the cost of capital in the Arab public sphere should be a serious consideration given its very real impact today in Cairo. Policy changes may incur short-term costs domestically, but the protests are yet another reminder that Israel's current strategy in the West Bank and Gaza is unsustainable. Israel is not to blame for the radical and dangerous actions of the protesters in Cairo. But there are political and diplomatic steps it can take to assure the integrity of its embassy and a better strategic relationship with Egypt in the future.