To be fair, while we can run controlled experiments on components of this problem, I don't think we can run a global controlled experiment of the entire system, or fully understand the long-term impact of climate change on humans in the face of advancing technology.
That problem exists for almost all innovative work. Generally, a paradigm becomes accepted when the predictions that follow from it are found to hold true. For people to make the effort to test such predictions requires (from a human standpoint) a "leap of faith", regardless of the integrity of the data that lead to said paradigm being proposed.
For example, it is now >50 years since anthropogenic global warming was first proposed. The first intergovernmental action I can find with a brief search that tackles climate change is the 1992 UN Framework Convention on Climate Change. Legislation surrounding CO2 emissions was not introduced until the 2000's. The matter is still "controversial".
https://en.wikipedia.org/wiki/United_Nations_Framework_Conve...