A good, and very pertinent question. This speculative and blunt answer is based on the literature that I have studied as part of understanding behavior change. It is a simplification of the literature, but it should set a foundation that you could build on if you wanted to investigate further and develop a more nuanced view.
Is religious affiliation really a predisposing factor for people to
actually commit acts of terrorism and politically-motivated violence?
I start with a basic assumption: As terrorists are people we can assume that they are motivated by the same things as people in general.
Based on this assumption it seems more than reasonable to expect that religious affiliation would influence behavior, and in some cases influence likelihood of violence and terrorism. In all that follows you can assume that I am contrasting one 'more benign' form of religious affiliation, such as atheism, with another form which is more easily used to justify violence, such as Christianity or Islam. The following are some reasons why having one type of affiliation rather than the other might affect behavior:
Mental characteristics, such as values, attitudes, and beliefs, have a strong influence on behavior [e.g. 1]. Additionally, these mental attributes are influenced by information [e.g., 2], such as what might have been encountered in religious literature. Given this argument, it seems reasonable to assume that the religious literature that terrorists have read could have influenced their mental attributes, and in turn predisposed them, even if just to a small extent, to engage in terrorist behavior.
Expected value has a strong influence on behavior . Essentially, people are more likely to engage in behaviours that they believe will create value for them. For most of us, suicide is a pretty low value outcome but for certain religions, suicide to kill others is going to be rewarded by eternal life, along with a number of devoted companions. Likewise a war can be holy for some religious affiliations but not others. In light of this example, it seems reasonable to assume that religious beliefs that make a terrorist behaviour appear like it will be more rewarding, will in turn influence people with those beliefs,than those without, to be more likely to engage in that behaviour.
Research suggests that most people generally require justifications for their actions to avoid congnitive dissonance [e.g., 4]. Those who have been raised by learning a religious scripture which presents many justifications for violence, would in turn have easy mental access to these justifications when thinking about how to act. Indeed, they might have access to the justification that a supreme, unquestionable, omnipent, ominpotent individual wants them to act in a violent way. Accordingly, it is reasonable to assume that individuals with these sets of justifications could use them to justify violence, while those not in possession of such justifications would not be able to.
I am happy to clarify, or add to this as you wish. I am sure I have oversimplified things in a few cases.
Ajzen, I. and M. Fishbein (2000). "Attitudes and the attitude-behavior relation: Reasoned and automatic processes." European Review of Social Psychology 11(1): 1-33.
 Chaiken, S. (1980). "Heuristic versus systematic information processing and the use of source versus message cues in persuasion." Journal of Personality and Social Psychology 39(5): 752-766.
 Wigfield, A. and J. S. Eccles (2000). "Expectancy-Value Theory of Achievement Motivation." Contemporary Educational Psychology 25(1): 68-81.
 Festinger, L. (1962). A theory of cognitive dissonance. Stanford, Calif., Stanford University Press.