And I have no problem blaming the ‘religion’ that breeds ‘islamists’.
Islamists and muslims - a distinction without a difference. Support one, you support the other. Muslims believe the words of the Koran, no? Perhaps you should read it and decide what it is that YOU believe.
Possibly there is no difference.
However, from a purely pragmatic standpoint we should do what we can to create a distinction. There are well over 1B Muslims on the planet. If we can crack some of them off from supporting Islamists, that is all to our advantage.
As an example, a great deal of the work on our A-bomb during WWII was done by Jewish and other German refugees from the Nazis (half of whom were working for Stalin, but that's another story). If we had insisted on defining our enemies as "Germans" rather than "Nazis," we would have lost the services of these men.