Medical studies with proper protocol and sufficient power are actually extremely reliable. Compared to the rest of the fields you mentioned, climate science is way more replicable and data-driven. The empirical evidence is so overwhelming that even the deniers no longer deny that the planet is warming. Now they have shifted the goalposts to quibble about whether this is 'man-made' or not. While harder to establish, there is abundant evidence supporting this hypothesis as well. It's also important to distinguish between this testing question and climate forecasting, which is harder and more error-prone.