There are some very hard facts in the climate debate that few, but the most partisan would debate. The radiation properties of CO2 for example as measurable in a laboratory.
Experts on specific areas will know these facts more accurately than the general public.
And then there are a great many issues, which are rather less hard. The ideal carbon tax at present from economic models is one example. This comes in from slightly negative to huge values of a thousand Euros per tonne C or higher.
I think it is the least hard facts, those relating to the effects of concrete policy measures that are the most policy relevant.
And I think that for those questions, the opinion of the public is perfectly in line with expert opinion. These are issues, where there is large uncertainty and a large personal values component, and reasonable expert opinion therefore covers a wide range and is not focused on a point estimate.