Many would say our political economy is built on insatiable consumption, and is therefore incapable of cutting emissions to such a scale to materially impact climate change. It makes no sense to blame 'Republicans' and/or 'Christians' for not trusting every proposed solution to these massively complex problems.
First, this isn't limited to politicians. Second, calling it a logical fallacy to believe what others say about themselves is utterly ridiculous and doesn't move goal posts so much as it pretends there are invisible goal posts swooping around the field at will and only you can know if the ball goes in.
Actually it is a logical fallacy to interpret one's rejection of a proposed solution to be a rejection of the problem. I'm not arguing any specific case for it, but it does seem to be quite common and problematic in civil discourse.
And the "another problem" is to misunderstand the way that money influences PR statements from powerful entities (politicians or otherwise). This part isn't illogical but just ignorant/mis-educated about wealth and power.
