Consider the SS and the firemen for a comparison. The SS believed without question. They had found order in Nazi beliefs and society, did not question it nor did they want to. The firemen, and Montag in the opening scene, were happy in their compliance with the law and their complicity in its enforcement. The idea that Clarisse would pose such innocent, fundamental challenges against the society they lived in is, at first, ludicrous to him.
I can definitely see similarities between the firemen and the Nazi army. The propaganda and social control are found in both the futuristic society found in the book, as well as the Nazi ideal. While one may have a difficult time tying Jews to "readers" in such a comparison, there are some clear areas in which firemen and Nazis are fairly similar.
To get the discussion going, consider the idea of comradeship: The nazis placed a great deal of importance upon national solidarity, and everyone subjecting themselves to the State's need for them. Similarly in the novel, members of the society were assigned vocations and encouraged to devote their lives to their work (i.e. Claire as a former, failed teacher, or the fire captain as not only a leader of firemen, but also a social leader who strove to convert his subordinates not only to their work, but also to the ideals that governed society.
Nazism ("National Socialism") and the culture found in Fahrenheit 451 both share the same political ideology of totalitarianism, in which the government controls all aspects of an individual's life, along with all aspects of trade and commerce. In such cultures, the greatest danger is anyone who would counter the established standards of the society; conformity and obedience are the key traits that maintain those in power. Any idea that has not been officially sanctioned is treasonous; certainly it would be forbidden to communicate ideas, and by extension, it would be preferable to forbid reading and burn anything written, as is the case in Fahrenheit. It's a member of the literary genre known as "Anti-Utopia" or "Dystopia; " Historically, during the 1930's, while the National Socialists in Germany were rising in power, any "heretical" written works not sanctioned by them were publicly burned. German poet Heinrich Heine (1797-1856) predicted the horrors of the German form of totalitarianism when he wrote the prescient phrase: "Where one burns books, one will soon burn people."