It cannot be denied that there is a veritable clash within Islam and between a certain aspect of Islam and the West.
The clash within Islam is between modernists and non-modernists. (Although Islamism is usually touted as the enemy, and whereas even modernist Islamists usually believe in and promote the superiority of Islam, the Islam that modernist Islamists believe in is usually modified to coexist with other religious and political systems or modified to adopt the values and standards of other religious and political systems, making that form of Islam more compatible.)
This debate used to be confined mainly among the higher levels of Islamic societies, among the thinkers and theologians and clerics, but because this debate has practical consequences for all Muslims, average Muslims are taking interest, speaking their mind, and campaigning for their preferred ideology.
This debate affects Muslims on two levels. The first level is at the personal level of practice and belief. Each side has a separate set of dictates as to what Muslims are supposed to do and believe. This is a matter of salvation and fulfilling the destiny of Islam, and so is important. Thus, average Muslims believe they have a right to participate in this debate because it affects which set of rules they will follow with regard to practice and belief.
The second level with regard to how this affects Muslims is at a meta level. Each side, along with dictating what a Muslim must do and believe, also dictates what sort of policies, laws, thoughts, ideas, and whatnot a Muslim polity must engage in. This significantly affects the way a Muslim polity relates with the world and how it organizes and administrates itself.
In reality, the debate boils down to one question that many of the other religions have answered (for the most part): is Islam a personal entity or a communal/political entity?
Note that a very significant issue in the debate is whether Islam can change or to what degree Islam actually dictates a polity’s policies and structure. While this is significant, the issue of being personal or communal/political is far greater because that will indicate to what degree a Muslim must exert himself in ensuring the application and spread of Islam (whatever Islam is said to be).