There was a recent finding (not yet replicated!) that performing rituals of any kind aids in building/retaining self-control/willpower.
This is kind of like priming, but—if it holds true—this result would actually take away a lot of the explanatory power of most priming studies. A simpler explanation than a bunch of specific "doing X makes you think about Y which makes you do Z" priming relations, is "doing {any number of things} releases striatal dopamine, that increases executive functioning, which allows you to do {any number of things}."
If you wash 5 times a day before prayers, yeah, washing your hands is going to put you in a mindset.
Or maybe I just don't understand what priming is.