I don't know if there is *a* right way.
My primary objective with net.discussions these days is to protect my own sanity. I've stayed up way too many nights, felt rotten on way too many days about stuff that really, ultimately, matters very little.
My secondary objective is to get the word out, whatever the word is.
If I find that it's impossible to talk to somebody without having my blood pressure shoot past safety levels, for whatever reason, I walk away (or try to; lately with perhaps a bit more success than some years ago). If I don't do that, I know what'll happen -- I'll blow a gasket and start ranting incoherently, very probably say something I'll regret, and will only feel more rotten about it than otherwise.
Hell, dte, take your fine self. I honestly *like* your fascist redneck stubborn self, but much of the time you drive me completely bonkers. We've been there. I've felt rotten about it, and I suspect that some barb of that may have penetrated even the pitch-black capitalist running-dog lump of coal that you have for a heart. What good did *that* ever do to anyone? Not a damn thing, I think.
So, I walk away. And come back. And we argue some more. And somebody's listening, maybe, and one day they'll be thinking that hm, that PJ sure is full of himself today, good thing we have dte to take him down a peg, and another day they'll be thinking that boy, did that PJ trip dte up but good this time. And, perhaps, little by little, a bit of it trickles through, and we understand each other just an iota better, or perhaps somebody reading gets something out of it, and it won't completely go to waste.
Not that I'm comparing you to any of the other people involved in this thread, mind, in any other way.
Oh, and, what if someone just isn't worth the trouble? If he's so irredeemably dishonest, stubborn, invincibly ignorant, and generally no fun at all that he's really not worth talking to? Then DON'T TALK TO HIM. Instead, talk to the general public -- deconstruct his/her/its arguments for public scrutiny. Point at the leaps of logic, made up facts, fallacious reasoning, and what have you, and giggle. The crowd will giggle with you, even if it won't make the slightest chink in said invincible ignorant's armor.
Also, do as I say, not as I do.