In what ways does al-qaeda, its religious and political views, and its methods pose a challenge to

For other Muslims, Alqaeda create challenges express disagreement with the US and Europe while still disapproving of the use of terrorism (moderate muslims believes that bombing other people simply because of different view couldn't be considered as jihad)
For Americans, Alqaeda create challenges to distinguish peaceful but unfamiliar principles in Islam from the misuse and abuse of Islam by terrorists.
This cause many people in western civilization to put all member of the religion into one basket and discriminate the people who actually want to create peaceful relationship with other culture.