Gingrich may well privately accept the overwhelming evidence supporting anthropogenic global warming. He’s supposedly regarded as a “green conservative” and tries to frame environmental issues in a conservative narrative.
Gingrich was also a Republican Presidential candidate at the time. He’d have been aware of polling information (what his potential voters want to hear), and the various signals from the right-wing media that either approve or disapprove of what he’s saying and endorsing. You’ll note that the woman in the video referred to Rush Limbaugh.
For Gingrich to have gained popular support from the conservative base, he would have had to disassociate himself from climate change—which he did. If you read some of the things he says on the matter, he comes across as very vague and non-committal. He either has to forget any principles and lie, or already disbelieve or be grossly misinformed about climate change.
Why is climate change such a politically polarising issue? Why are conservative Republican voters less likely to support a candidate who endorses action against anthropogenic climate change?
There’s quite a sophisticated system of propaganda in the US. The US is a business run society where everything from popular culture to the media is shaped to suit capitalist interests.
The most popular media sources are profit driven and corporate owned, and this leads to framing narratives and restricting the discourse to various “issues” that happen to suit rich elite and corporate interests. These same elites and corporations also happen to influence the political process through campaign donations and lobbying of government.
The end result (I’m skipping a lot of analysis for the sake of brevity) is an illusioned public who become polarised around various emotive “issues”, but never really question the underlying system. Politicians, who represent the rich and various corporate sectors, say things that their particular voters and potential voters like to hear—and those voters like to hear what they want to hear, because their opinions have been shaped by the very corporate media that they rely on.