Only a few percent of the population understand science in general and even fewer understand those particular branches of science involved in the acceptance of evolution or climate change. So of course when you examine the beliefs of a population, knowledge is only weakly correlated if at all.
Certainly if I don't know a sport, I'm not qualified to choose an all star team or to make a guess about which team or athlete is best. Same with science.
However, IQ is highly correlated with acceptance of evolution and the 4.54 billion year age of the Earth. And it's inversely correlated with accepting the Bible as the literal truth.http://www.dailymail.co.uk/news/article-2395972/Atheists-higher-IQs-Their-intelligence-makes-likely-dismiss-religion-irrational-unscientific.html
But even the high IQ people may not know much about a specific scientific discipline. There's too much knowledge out there to be an expert on more than one or two disciplines.