At the time, priests, seen as corrupt, would visit the villages they governed, demand a feast, and ate gluttonously from the resentful but obliging, heavily taxed subjects. Rising anti-clerical sentiment led to cloaked ways to carefully express the residents dissatisfaction of this unfair system of governing, hence, the creation of "Strozzapreti". The clergy would eat this thick, chewy pasta and it would either keep them from talking so much, fill them up so there wouldn't be enough room for the main courses, or they would literally choke on it from ravenously eating.
Not to fear, though! It is a wonderful pasta with a dumpling like texture that has endured for centuries as an Italian classic.