Here is a paper on how climate change deniers have to believe multiple contradicting things to justify their position.
There is considerable evidence that the rejection of (climate) science involves a component of conspiracist discourse. In this article, we provided preliminary evidence that the pseudo-scientific arguments that underpin climate science denial are mutually incoherent, which is a known attribute of conspiracist ideation. The lack of mechanisms to self-correct the scientific incoherencies manifest in denialist discourse further evidences that this is not the level at which rational activity is focused, and we must move to a higher level, looking at the role of conspiracist ideation in the political realm. At that political level, climate denial achieves coherence in its uniform and unifying opposition to GHG emission cuts. The coherent political stance of denial may not be undercut by its scientific incoherence. Climate science denial is therefore perhaps best understood as a rational activity that replaces a coherent body of science with an incoherent and conspiracist body of pseudo-science for political reasons and with considerable political coherence and effectiveness.