1. Republicans live in the suburbs and live a "high carbon footprint" lifestyle and thus will bear more of the economic incidence of a higher carbon tax than center city progressives. So, the average Republican faces a higher price if the carbon tax is enacted. See my papers here and here. In a differentiated products model, Republicans may gain greater consumer surplus from their light duty trucks and monster cars while progressives enjoy their fuel sipping Priuses. In my model, Republicans know what they want from markets and they perceive that progressive regulation will raise the price tag of the red meat, monster car, blasting air conditioner on hot day life style.
2. Republicans are more likely to work in "high carbon industries" (oil and other fossil fuel extraction industries) and thus may face greater unemployment risk from regulations that make these industries less competitive. Republicans are also more likely (I bet) to own shares in these companies such as Exxon and thus will suffer a capital gains loss from carbon regulation.
3. Republicans may be more optimistic about their ability to adapt to climate change. Progressives have a greater trust in government while Republicans tend to believe in individual freedom and smaller government. If Republicans are more optimistic about their ability to individually adapt to the new challenges of climate change, then this would mean that their benefits of carbon mitigation is lower than the benefits that progressives believe they would gain.
Note that my explanations here have a very different vision than the more sinister NY Times narrative. I am explicitly discussing the self selection of Republicans into specific geographic areas and specific cities (Houston) and industries. The New York Times needs to think more carefully about the diverse mix of Americans and how each of us makes choices based on our own conception of the good life. The New York Times wants to argue that the Republicans have been duped by expert manipulators. That's an interesting theory but my theory is more plausible. I agree with the NY Times that John McCain's efforts in 2008 to build a Republican coalition supporting carbon mitigation efforts was laudable. For any politician, there is always an issue of why voters back him. If a candidate takes a stand on 200 positions, his supporters may agree with him on 4 key ones and ignore his views on the other 196.
Note that my theory does not invoke "crazy beliefs" or ingesting "fake news". Instead, my theory rests on pursuing self interest.
UPDATE: Jonathan Eyer makes a nice point related to point #2 above. He says that progressives (think of Twitter) work in industries that are less affected by future climate change while agricultural interests will be more affected by future climate change. I would say that the costs of climate change are uncertain and in the future (and thus are discounted). Voters who are risk neutral will downplay these. Yes, I know the literature on "fat tail" risk but the Weitzman fat tail argument ignores spatial economics. We can retreat to Montana. There is no "Montana" in the one sector growth model that Nordhaus and Weitzman use. Read my 2014 lecture.