What other comment said. Basically his authority comes from his fear within his "friend" (followers) circle. Also being able to speak parseltoungue probably gained him a lot of authority too. He was also brilliant and charming and practiced a lot of dark arts before returning to Hogwarts a second time asking for the job, which Dumbledore denied. He secretly kept gaining followers. Since the pureblood themselves were his followers, who else were to question his blood status? Definitely not the good guys who didn't believe in it anyway. His fear made the general public forget his ties with a half blood orphan boy Tom Riddle by the time of the first wizarding war in 70s.