Or are you suggesting that the invasions of Iraq / Afghanistan can be seen as "attacking their culture"? If that's your point, you've actually demonstrated that the root cause is in fact religion, because there really isn't much else that Afghanistani and Iraqi culture share with Egypt and Libya..
Gaddafi was hardly a beacon of good government, but debt-slavery to the IMF and open doors to the ransacking of national resources by western corporations is hardly an improvement. Not to mention little things like the incidents of ethnic cleansing.
Anyway, I reject your premise. To win that war they had to have wide support from the general population of Libya - there were no foreign troops on the ground, it was Libyans fighting Libyans.