Disagreement is a part of life.
It is everywhere. There is nothing you can do to avoid it. There will always be someone that has opposing viewpoints, opposing beliefs, or does things a little differently than you. It's not your job to fix it.
You can't change people.
Some people are under the assumption that being rude will cause a person to "wake up" and understand that what he or she thinks is incorrect. Unfortunately, that only hurts the situation more. It does nothing more than fuel the fire in an argument and veer the disrespect to a more personal level...and for what? You think you've made your point?
Who do you think you are?
You have no right to judge others' beliefs. Period. You don't need to be the person to deliver a punchline response because it's probably not your place to do so. Some people relish in putting up a fight, especially within social media. Admittedly, it is easier to think and say what comes to mind when you're sitting behind a screen; I've fallen into that trap. However, there is a limit. Until you've walked in a person's shoes, you're not the person to tell them they're wrong to think the way they do.
Sometimes silence is best.
It shouldn't be a goal to stir things up. I think it is safe to say that most people don't have enough background on a topic of argument before blurting out something offensive. Also, why fight just to fight? It's okay to ignore something that you don't agree with and avoid that negative conflict.
It's OK to defend yourself.
You should feel comfortable defending yourself but not be absentminded enough not to recognize that the person you're having an argument with has his or her own set of beliefs. I'm not saying that you shouldn't voice your opinions and offer valid, argumentative statements. Every person should be able to stick up for his or her beliefs, but not for the expense of showing hate. It is not wrong to give people something to think about, though. But if you're wanting someone to soak in what you have to say, disrespect is not the path to take.