WASHINGTON — Walid Jawad was tired of all the chatter on Middle Eastern blogs and Internet forums in praise of gory attacks carried out by the “noble resistance” in Iraq. So Mr. Jawad, one of two Arabic-speaking members of what the State Department called its Digital Outreach Team, posted his own question: Why was it that many in the Arab world quickly condemned civilian Palestinian deaths but were mute about the endless killing of women and children by suicide bombers in Iraq? Among those who responded was a man named Radad, evidently a Sunni Muslim, who wrote that many of...