Ask yourself this. When a sword comes swinging through the air, what takes the least amount of damage, the rock or the water? The rock is hard and strong and will try to battle the sword directly, but this impact will break both the rock and the sword, water on the other hand flows and simply moves around the sword, it doesn't really get damaged, both the sword and the water remain. "Standing up" to furries is like being a rock, you're taking the criticism head on and trying to fight back, but it's just gonna cause problems and honestly just make you look more like a fool.
To stand up to furries, you need to be like water, maneuver around the insults. They may call you a freak, ask them why they think or just go "Yeah, I'm a freak, what of it?". When someone insults you they're trying to get a reaction out of you, trying to make you angry, trying to make you sad, they think it's funny! If you try to stand up for yourself, call them names, do whatever, you're giving them exactly what they want, to them you are weak, you are evil and you are the enemy. IF you don't give them the reaction, you be polite or you simply just act like you don't give a **censor** what they think (Note: That does not mean saying "I don't care what you think", it's like saying "uh-huh, whatever you say"). Just flow around the insults, show them they don't matter to you.