While the author does not clearly state his atheist perspective, it is pretty clear that he considers religion, per se to be the problem, not merely certain fanatical adherents of one particular religion known as Islam:
Not a war of one religion against another, but of reason against religion--against any belief system that takes its mandate from an invisible spiritual entity and endows its followers with the right to murder or subjugate anyone who fails to come to the same conclusion.
Thus, he makes a false distinction between reason and religion, and he further characterizes religion (again, per se) to mean murdering and subjugating in the name of some 'invisible spiritual entity'. Excuse me if I draw the obvious conclusion that the writer is hostile to ALL religion, not just Islamic terrorists.
As for the 'cult of rationalism', this simply describes the mentality of Randians, followers of Md. Murray O'Hare, the publishers of Skeptic magazine and many outspoken atheistic scientists who tout human reason as the highest standard in all things and often like to spell it with a capital 'R'. I do not mean that there is an organized cult or official religion, nor was it meant to be derogatory. The simple fact is that there are many people who, lacking a belief in God, substitute Reason as their god and habitually castigate all religions and all religious persons for the atrocious acts of a few extremists. However, they would be loathe to take the blame, as atheists, for all the atrocities committed by atheists throughout history (French Revolution, Marxism, Marque de Sade, etc.) Gee, THAT would be unfair, wouldn't it?