I can speak from experience and with a strong interest in Turkey that the level of animosity Turks have felt toward the US has little to do with our support for Israel.
Although I cannot comment on the rest of the Middle East, Turkish anger toward us really did begin to rise with our invasion of Iraq in 2003. Let me take you through an anecdotal and off topic series of visits to Turkey: I first visited Turkey in 2001. While there, I met a woman who absolutely loved Clinton (she was very jealous of Monica, j/k) and most Turks I met remembered him kissing a baby or something after the earthquake in 1999. Our popularity polls were quite high at the time and people were very sorry for the USA during 9/11. My next visit was in 2002 and by this time talk of invading Iraq was in full force. My future father-in-law told me a joke about Osama bin Laden beating George Bush. He thought it was funny and I took it as being a bit hostile. My most eye-opening visit was in 2007. I had visited a small pin factory where a Turk and Kurd happened to be working. The Kurd loved America and kept telling me how wise he thought George Washington was. The Turk called all Americans murderers for what we were doing in Iraq.
What might explain this change in attitude? Not Israel. There are several other reasons for their anger during this time period. Here are a few of the grievances I read about in Turkish news or heard from Turkish friends in the time frame from 2002-2009: America treated the Turks like servants who would do whatever we wanted with respect to invading Iraq, we capture 5 Turkish soldiers in Iraq and blindfold them (later becomes the subject of a widely popular movie), freed up the PKK in Northern Iraq to continually attack across the border, supplied American rifles to the PKK, increased rhetoric on Armenian genocide bills, and have generally showed little concern for Turkish interests in the region.
Anger toward us is based entirely on our policies, or their perception of our policies, toward them. This is probably true of any group in the region.