Someone who is incredibly vulgar, hateful, and spiteful all the time -- for no reason. Typically, an offensive monkey has no idea that people feel this way about them because they are disconnected from reality.
But you gotta be careful around offensive monkeys, because they are crazy and could snap at any moment, without warning, and bite your fingers off and/or tear your face up.
Sam: Can you believe that douche?
Nick: Yeah man, what an offensive monkey.