Usually, if you have to argue, you are at a loss.
That is why I try to stop being an argumentor and try to be an educator instead. If your educational arguments hit people that are not already defensive about you or that particular subject, you have the chance to change their minds (your arguments that is, it should not be you who manipulates them to believe what you believe). You have to help them discover for themself their cognitive dissonance on certain, as many people (maybe all) have good intentions but bad strategies to implement them.
Climate change deniers are like anti-vaxxers, they have good intentions (for the economy/society or their children), but fail to go beyond the intuitive response (short-term inconvenience/pains) as a sacrifice for long-term gains (sustainable planet, overall protected healthy kids).
We have to recognize first that they are well-intentioned, because if we alienate them, we just drive them towards more extreme positions, where religion, climate-change denial, gun ownership, islamophobia, free speech and GOP all lump together and become unseparable as a group identity of the frightened and attacked.
This is not only a rightwing problem btw; on the left we have the same with a lumping together of alternative medicine-vegan-glutenfree-Anti-GMO-homeopathy-anti-vaxxers-detoxing-social-justice-warrior-safezone-outragers that are just as crazy and Dunning-Kruger as the worst of the right.
So yeah, moderate but factual speech is needed against the outrage news economy; and education as a safeguard to prevent the once rescued from falling back into the irrational jungle.