Regardless of what _____ theories of politics may propound, there is nothing that requires daily politics to be clear, thorough, and consistent—nothing, that is, that requires reality to conform to theory.

Regardless creates a contrast, and the rest of the sentence emphasizes that there is nothing that requires daily politics to be clear, thorough, and consistent. If politics need not be clear, thorough and consistent, that means they are unclear, not thorough and inconsistent. The contrast created by regardless ensures that the word for the blank should consistent. clear and thorough. Thus theories should be propounding that the politics should be tidy and orderly. So C and E should be the correct answer.

But again, logically speaking, a tidy theory may propound chaos, and an untidy theory may advocate order. So, in mu opinion, this is not a good question. In fact, it is not an ETS questions.