Webster - Shmepster
You know the connotation of the word when it is used in that fashion. The way you are using it grew out of the political party and the control that they attempted to exert and the horror that they brought to this world towards that end.
I wasn't trying to call you out or anything, I just wanted to voice my opinion that would could refrain from words that may hurt others. If you feel comfortable using it in that fashion then you have every right. Let's just say that it is not a phrase that I prefer to use.
And just because you asked this is from dictionary.com - I like how #3 says "sometimes offense" and you did use it lowercase.
1. a member of the National Socialist German Workers' party of Germany, which in 1933, under Adolf Hitler, seized political control of the country, suppressing all opposition and establishing a dictatorship over all cultural, economic, and political activities of the people, and promulgated belief in the supremacy of Hitler as Führer, aggressive anti-Semitism, the natural supremacy of the German people, and the establishment of Germany by superior force as a dominant world power. The party was officially abolished in 1945 at the conclusion of World War II.
2. (often lowercase

) a person elsewhere who holds similar views.
3. Sometimes Offensive. (often lowercase

) a person who is fanatically dedicated to or seeks to control a specified activity, practice, etc.: a jazz nazi who disdains other forms of music; tobacco nazis trying to ban smoking.