Stiff is merely a nickname, its rather a tease instead. As you know, Erudite feel the need to be rude towards Abnegation. The nickname Stiff is commonly used as Abnegation wear plain, grey clothes to be humble and subtle - grey is also their faction colour displayed by the grey stones used to represent Abnegation at the choosing ceremony.
People who call Abnegation Stiffs are referring to the way the members of Abnegation don't indulge. An example of this would be the fact Tris hadn't had a hamburger before because that would be self-indulgent.
Erudite's hate is displayed in some rather vicious reports released by Erudite against one of Abnegation's Leaders- Marcus, the Father of Four. These reports implicate that Marcus' abusive behaviour towards Four, was the reason for Four to change from Abnegation to Dauntless. The reason that Erudite does this is to suggest Erudite being better as the Government over Abnegation.
Also,in in some respects fighting back when people insult you could be considered self-indulgent so that makes Abnegation a easy target.