The comparison between YEC and evolution falls flat on its face because of the actual physical evidence in support of evolution where creationists have to call upon acts of god to support their hypothesis. It was god who put the dinosaur fossils in the soil to test the faith of his flock, it was god who twisted the laws of physics in such as way as to make it possible for cosmic background radiation to appear to show the universe as it looked ~14 billion years ago, etc. This dichotomy does not exist in the debate between the proponents of a climate catastrophe and those who do not hold with this hypothesis. Both sides call upon what they see as evidence for their stance, in this case the evidence mostly consists of models. Those models are both coarse-grained and limited in the factors they take into account. When tested against historical data the models have shown to grossly overstate the warming effect, they also leave out some important factors like cloud cover where a ~2% increase in cloud cover can negate the calculated warming effect so it is definitely a factor which should be included.

Creationists are driven by religion. They may claim that evolution is also a religion but that is just playing with words and has no relation to the stand-off between those who support the climate catastrophe hypothesis and those who don't. In the former case religion was the main driver from the start, in the latter the movement got its start based on scientific studies. The current climate catastrophe hypothesis is not the first, there have been several predecessors. Some of these got some traction - the global cooling scare of the early '70s is one of these - while others languished. The religious undertone only became a factor in the current climate catastrophe hypothesis when it was picked up by mass media, celebrities, politicians and business interests who latched on to some parts of the IPCC reports and ran with it. Where the normal discourse in science, although heated, still remains open for discussion and by necessity for falsification, the non-scientific proponents of the climate catastrophe hypothesis had and have no such qualms. It is from there the claims of '97% of all scientists agree' and 'we only have 10/12/15 years left' arise, is is that group which coined the label 'climate denier'. The involvement of political groups in positions of power has made it a potentially career-limiting (or rather 'funding-limiting' but it comes down to the same thing) proposition to openly go against what is now becoming the dogma of the looming climate catastrophe.

This is not how science works. When a model has been proven to give the wrong results you adjust the model, you don't base policy on it. The models used by the IPCC have shown to overestimate warming by a large degree so they clearly are not showing the whole image. The reasons for the over-estimation can be several, most likely though is that the models don't take a limiting factors into account, cloud cover being a possible candidate. Instead of silencing those who follow the normal scientific method by falsifying a hypothesis these results should be taken into account and weighed for their validity, even when they come from a group which is ideologically opposed to yours.

Climate change is a real thing in the past and present, there is hardly anyone who denies this. Catastrophic climate change is a hypothesis. Anthropogenic catastrophic climate change is another hypothesis. The path from hypothesis to theory goes through attempted falsification, there is no other valid way. When presented with what is claimed to be a successful falsification the reaction should be to test it and when found valid lead to something like "well that is interesting, it looks like we missed something" instead of "go away heretic, we don't need your type around here". The former leads to better science, the latter to Lysenkoism.