I think people overestimate the role of religion in their lives, to the risk of denying themselves agency. MLK, to take an drastically different example, often spoke of being inspired by religion. But - with the greatest of respects to the good man - I think underestimated his own inherent goodness. If MLK was an atheist or irreligious, would he have been less motivated to fight racial and economic inequality? Somehow I doubt it.
I tend to think that, barring extreme circumstances like a politician converting to a cuase just before an election, we should accept that the motivations people say they have are the motivations they actually have. If someone like Martin Luther King or Maximilian Kolbe says they were motivated by their christian beliefs, they probably were. Similarly, someone who burned heretics was probably motivate by their christian beliefs.
As a Catholic, I have no problem accepting that someone like Torquemada (I don't know enough about the Inquisition to say whether it was theology or court politics or something, but theology no doubt motivated some people) was inspired by his Catholicism as Kolbe was. I'd then go on to say that his Catholicism was a complete perversion of the gospel, but that's not relevant to whether christianity motivated him.
In the same way I don't think it's sensible to say that every terrorist atrocity can be reduced to one of or a mixture of psychology or economics or politics. Theology plays a part. But we can say that without saying Islam is always and everywhere violent and oppressive.
