http://www.m-w.com/dictionary/fascist
1 often capitalized : a political philosophy, movement, or regime (as that of the Fascisti) that exalts nation and often race above the individual and that stands for a centralized autocratic government headed by a dictatorial leader, severe economic and social regimentation, and forcible suppression of opposition
2 : a tendency toward or actual exercise of strong autocratic or dictatorial control <early instances of army fascism and brutality
Here’s another:
http://encarta.msn.com/encyclopedia_761568245/Fascism.html
Fascism, modern political ideology that seeks to regenerate the social, economic, and cultural life of a country by basing it on a heightened sense of national belonging or ethnic identity. Fascism rejects liberal ideas such as freedom and individual rights, and often presses for the destruction of elections, legislatures, and other elements of democracy. Despite the idealistic goals of fascism, attempts to build fascist societies have led to wars and persecutions that caused millions of deaths. As a result, fascism is strongly associated with right-wing fanaticism, racism, totalitarianism, and violence.
Now replace race with religion.
Then what exactly doesn’t fit?
The second reference has much, much more detail if you care to read it.
Now replace race with religion.Considering you've just completely changed the meaning of the term you could say it doesn't "fit".
Then what exactly doesnt fit?