Quick note. @Brythan gives a very good answer on personal choice. Political choice is somewhat different.
Politicians are different. They have advisors. They have experts and it's just not possible that so many on the right actually believe what they say they believe on Climate change.
Politicians lie and they spin. This should be news to nobody.
Politicians also have a staff and the better ones, have a staff that studies the facts, not a staff of yes men. That's politics 101 going back to Machiavelli. Lincoln was also big on having people who disagreed with him near him. And whatever some people say and whatever individuals believe, the evidence is very strong that climate change is real and man made. It's simply not possible that most congressmen don't know this.
So when they talk about it and they say there's no proof, or they say it might be natural, or when James Inhoff brings a snowball inside and throws it on the floor - they are lying. Period. Straight up fact. At least the smart ones are.
Why do people believe that efforts against climate change are futile
even though they accept that the climate is changing?
Now, they can claim in a Bill Clinton I didn't have sex way that "it could be natural, not man made", and statistically, there's about a one chance in 10,000 that this is the case. But at the very least, it's spin.
So, why do they spin?
It comes down to, approach/desired outcome over truth. Very few politicans say everything they believe. They will often say things to work towards an outcome they are after. "You can keep your doctor" for example. Which was actually true, if your company kept the same plans (many didn't).
In 2001, when IPCC-TAR came out, and the scientists behind the report said "We're 99% sure it's real and man made", I guarantee that President George W. Bush's advisors told him that the scientists were probably right and that climate change was probably real and man made. (Maybe not Cheney). Bush in 2007 or 2008 said Climate change was real. Donald Trump in 2009 endorsed a memo to the president that said climate change was real and action needed to be taken towards clean energy. The evidence that climate change is real and man made has grown stronger since then
Why do they spin it this way?
1) For their constituency (and lets not forget special interests).
2) Because if they admit it's real, that implies that action should be taken and relevant actions involve things conservatives generally don't like. Regulation, Taxes and 3rd world financial support.
A related problem is that Climate change is very big and the solution requires enormous change and huge financial effort. It's not a simple fix at all. A 75% reduction in Co2 footprint, globally, combined with desired 3rd world economic growth, that's just bonkers difficult.
So it's much easier to say "It's not real" or "it might be natural", or "more study is needed", because admitting it's real and fixing it, is a big noisy mess. Much harder than healthcare.
So "It's not real" - it's the easy way out. It's a lie, but it wins points with their constituency and it steers the conversation and political actions closer to what they want.
Problem - it's a lie that's not going to work forever. Man made climate change is real and it's progressive. We will see it get worse. so the "We don't know", isn't going to fly forever, but it's a short term fix.
There were oil company memos that address the reality of man made climate change that are 40 years old. Doubting the science is foolish. The science remains unchallenged for 40 years, not in any peer reviewed or evidence backed way and if it wasn't true, finding evidence to the contrary would be fairly straight forward. It's just temperature and circulation. It's not magic.
Any interesting question that may arise in the not too distant future, is "why did they lie". The denial can't go on forever, not for something that's real and growing.