If they are hostile from the very instant they quoted me, I don't even bother a response.
If they quote me with genuine interest, I do my best to explain my views, if they become hostile during the process, I stop responding.
If they stay civil but we're just not going to agree, I tell them "It doesn't look like we're going to agree on this, but I've enjoyed our conversation." and then I stop responding.
A lot of arguments aren't even about the OP anyway, they start about the OP and then go wayyy off-topic or they're about some minor thing somebody through out and the whole argument starts off-topic.
I don't mind a contrasting viewpoint, how am I supposed to learn, change or strengthen my own stance if my views are never challenged? I would just prefer to do so with a person who also wants to have a conversation, rather than win. I have no problem saying "You're right, thank you for the correction" or if it's based on a misunderstanding "I apologize, that was not my intention".