Culture war. And not limited to a struggle between Muslims and Jews (plus "the West") but between neo-caliphates and everyone they consider kufr, including Muslims.
Al-Qa'ida's goal is to "unite all Muslims and to establish a government which follows the rule of the Caliphs." Bin Laden has stated that the only way to establish the Caliphate is by force. Al-Qa'ida's goal, therefore, is to overthrow nearly all Muslim governments, which are viewed as corrupt, to drive Western influence from those countries, and eventually to abolish state boundaries.
There is no question that a sizable portion of the Muslim world considers it to be a religious war.
I always get a chuckle at how misinformed a sizable portion of the Muslim world is about many things. Most of which comes from their clerics - giving many non-religious (in fact anti-Islamic) teachings a religious color.
In the Muslim world culture is inseparable from Islam.
Devout Muslims consider the Koran to be a comprehensive instruction book on the business of living one's life.
Except for religion the non-Muslims living in the Middle East share most of the cultural traits as the Muslims, but they are not at war with the West.
No, this is a religious war.