There was a time when Republicans embraced the cause of environmental protection. Think Progress noted that “some of the greatest conservationists ever to take the oath of office were Republicans.” Both Greenpeace and the Union of Concerned Scientists rated Richard Nixon one of the greenest president ever.  And we're not talking ancient history here: both Presidents Bush supported cap and trade policies to reduce pollution.

So what happened? What happened is that the environmental movement was taken over by anti-business purists who essentially vilified their detractors as amoral worshipers of profit and consumption willing to destroy the natural world in relentless pursuit of the almighty dollar.  Consider, for instance, the evolving rhetoric of the Sierra Club and its members:

“By continuing to choose talk over action and political compromise over strong advocacy the directors are failing in their mission to protect the environment for future generations and are selling our members short.”

“We cannot afford to compromise with those who exploit public lands for private profit. We cannot afford to trade our children’s future for the illusion of political access. If we do, we will have nothing left.”

- Sierra Club “renegades” quoted by Leora Broydo, Mother Jones, Mutiny at the Sierra Club, November 1, 1998

“If you are the Sierra Club, what would you call a senator who: a) voted against oil drilling in the Arctic National Wildlife Refuge; b) introduced legislation to cut greenhouse gas emissions; and c) co-wrote a 3.5 million-acre statewide wilderness bill?  Answer: the enemy.”

- Joel Connelly, Seattle PI, “Sierra Club throws a sucker punch” March 2, 2008

“Civil disobedience is the response of ordinary people to extraordinary injustices,” the group said in a statement before the protest, casting the climate debate as akin to previous struggles over “slavery, child labor, suffrage, segregation and inequality for gays and immigrant workers.”

- Talia Buford, Politico, “Sierra Club goes Bolder” February 23, 2013  

Here we have a message: if you don't agree with us, you're no different than an apologist for slavery and child labor. If you don't get with our program, there will be no future for our children.

Is it any wonder that a lot of Republicans soured on the environmental movement or came to doubt the "consensus" on climate change? Sure, as members of a pro-business/limited government party, it's not surprising that Republicans would be a bit less gung-ho about environmental regulation than Democrats. But that doesn't explain the change in Republican opinion over the last decade or so.  Check it out:

Partisan Gap on Environmental Regulations 2.png
Partisan Gap on Global Warming 2.png

Notice that the partisan divergence on environmental regulation coincides with the Great Recession. It actually makes a lot of sense to me that people would be more concerned about the impact of regulations on jobs and the economy when the economy is tanking. The fact that Democratic opinion didn't budge much in response to the economic tailspin and its prolonged aftermath must have reinforced Republican suspicions that Democrats/environmentalist are indifferent to the reality of their everyday lives.

As for global warming, I agree with Justin Fox, who pointed out that for years Democrats and environmentalists have misrepresented the scientific consensus for political ends, which has created a backlash. As Fox puts it:

...there is no scientific consensus about how dangerous climate change will be, nor what should be done about it....When people try to use the 97 percent [consensus] figure as a debate-ender on climate policy, they're adding political content to a scientific finding. It shouldn't be all that surprising that others then react politically.

References:

Justin Fox, Bloomberg.com, 97 Percent Consensus on Climate Change? It's Complicated. June 15, 2017

Monica Anderson, Pew Research, “For Earth Day, here’s how Americans view environmental issues” April 20, 2017