Brony nazis are mostly responsible for flaming chatrooms and spamming image boards on topics relating to MLP, especially where such topics are undesired. Generally, they are more aggressive than hardcore bronies by going far beyond than simply proclaiming that they love the show. This generates annoyance in non-bronies and rather than making them convert into bronies, actually delays such conversion instead. As a result, brony nazis often fail to accomplish their "duty."
Brony nazis who support a certain generation of MLP display hatred against the other generations of the show. This is most common for those who only like the G4 MLP:FiM. Because of this, many videos of G1, G3, and G3.5 on YouTube have a staggering ratio of dislikes:likes, with satire and ridicule filling up the comments.
In a sense, brony nazis are anti-non-bronies, misusing the Elements of Harmony for mankind.
Keep in mind that not all bronies are brony nazis, but beware of those who are. As a rule of thumb, avoid talking to them and people who are potentially brony nazis to save you many nights of headaches.
Me: Oh hey look, a G3 related video on the right... >_>
G4 Brony Nazi: BURN IT WITH FIRE!!!
Me: Hey! Love and tolerate! D:
2. Brony: OMG, MLP:FiM is SO AWESOME! /)^3^(\
Person: Dude, chill. It's just a cartoon. What's the big deal?
Brony: The big deal? (starts posting pony pictures)
Person: No! I shan't succumb to such faggotry!
Brony: What?! HOW DARE YOU!! THIS CALLS FOR EXTREME MEASURES!!!
Person: Oh shit, a brony nazi! (leaves chatroom)