There are no rules for things like that. Language is always shifting and ever changing. Linguistically, there are no rules provided that meaning and communication is acheived. There are no "inferior" dialects and no "wrong" words - unless meaning is broken. And, as far as I've seen, the usage of Nazi as indicated here has been around for quite some time and is common. The Soup Nazi has already been mentioned a lot; there's a reason they did that, though it helped popularize it.
As for the OEDs (Oxford english dictionary) entry, it was uncharacteristically subpar. They actually included some form of the root word in every definition.
Here is a definition of Nazi that they list:
" b. hyperbolically. A person who is perceived to be authoritarian, autocratic, or inflexible; one who seeks to impose his or her views upon others. Usu. derogatory.
1982 P. J. O'ROURKE in Inquiry 15 Mar. 8/3 The Safety Nazis advocate gun control, vigorous exercise, and health foods. 1995 Independent 3 Nov. (Suppl.) 8/2 According to Hutchins, current fitness theory is peddled by ‘nazis’. Aerobics Nazis. 2000 Minx Aug. 71/2, I learned to be more open and not such a Nazi in the studio."
I've included its first known usage. 1982. So yes, it is acceptable.