OE


You need to read at least the second sentence before attempting to fill in the first. We are told that we like to think of ourselves as firm in our beliefs, when in truth those beliefs are easily swayed. The first blank, therefore, must refer to this susceptibility to external suggestion. Dogmatic is nearly the opposite; it means opinionated or asserting opinions in a doctrinaire manner. Fatuous (foolish) is better, but is a bit too judgmental - eliminate it. You are left with tractable, which means easily managed or yielding. In order to fill in the last two blanks, you need to have some sense of what the sentence as a whole is saying; the gist seems to be that participants in the Asch study misjudged the length of a line in the interests of conformity. For the first blank, then, we need a word that means something like ignore.
Vituperate (vilify or berate) makes no sense in this context; there is no suggestion that the participants actively criticized their sensory perceptions. You have probably heard the phrase garner evidence before, but do not be led astray; to garner means to gather, which does not work here. To repudiate, on the other hand, works well; it means to reject or to refuse to acknowledge.
Finally, we need a word that means something like agree with to fill in the last blank. To preclude means to make impossible, while to quibble with means to make trivial objections; neither makes sense in this context. Abide by (to act in accord with or to submit to) is the correct answer.