You can't change anyone. You can't get anyone to abandon their position and take up yours. Its not because they are stupid, its not because they need to "wake up" and its not because you just aren't persuasive enough. People just don't change.
Unless they want to.
See it doesn't matter how great your blog post is, or how awesome that captioned image of Obama you just posted to Facebook is, you aren't going to change anyone's mind (let alone their heart) with it. People are stubborn. We're subject to such things as confirmation bias, the backfire effect, and cognitive inertia. We are defensive and reactionary, and there's not much that other people can do about it.
You can make your opponent look stupid by lampooning their position, that just makes them defensive. You can make your opponent look evil by claiming the moral high ground, that just makes them angry. You can can debate your opponent and counter every point they offer, that just makes them determined to do better next time. No change of mind or heart will occur.
So what do we do?
You love them. The best way to get someone to pay attention to your ideas is to love that person. Its easy to ignore someone who is attacking you, its much harder to ignore the person bandaging your wounds. Its hard to deny the goodness of the worldview held by a saint.
When Proverbs 25:21 says to feed your enemies, and verse 22 follows by saying that by doing so you'll "heap burning coals upon his head" that's not to say that you'll be getting some sort of strange revenge over your enemies. Fire purifies, and the coals will purify your enemy's head, i.e., your kindness, your love, will win him over.
Admittedly it feels much better to ridicule or win a debate, but if that's the path you take you already have your reward. If you love your opponent you may win yourself a new brother. It takes time, and consistency, and turning the other cheek, but it is the only way to effect real change in another person. You can't debate someone into seeing the light! You can't ridicule a sinner into a saint!
So show people love. You may not win them over now, or ever depending on the hardness of their heart, but its the only way to even have a shot.