I'll bring up this analogy again, because I think it's a good one.
Nobody knows exactly why cigarettes cause cancer. There are many likely candidates: carcinogens destroying cells and causing genetic mutations...the presence of specific compounds which trigger uncontrolled dividing...many reasons that seem plausible, even likely. Nobody can predict with any certainty which individual smokers will get lung cancer. Some smokers can smoke a pack a day for 50 years and die of old age. Some get lung cancer having never smoked at all.
However for a sufficiently large group, very accurate predictions can be made. Computer models have been developed which can accurately predict cancer, emphysema, and heart disease rates per capita in different countries with astonishing precision. Models can accurately predict the percentage of smokers suffering from these diseases as a function of the total number of smokers, even going back in the past.
Nobody argues anymore that smoking isn't detrimental to the health, despite the fact that we can't explain the underlying mechanism with 100% certainty. Nobody decries studies of the disease rates amongst smokers as bunk or flying in the face of the scientific method. Nobody says its ok to just keep smoking because the underlying mechanisms are unknown (although if you go back to the 50's, one does see a large business-centric campaign of misinformation on the part of cigarette manufacturers).
Climate modeling is similarly sophisticated (and I would argue it is far more so): modern models can combine hundreds of distinct, measurable factors, and using stochastic modelling can predict global temperatures in a region-accurate way with a high degree of precision. Rewinding these models through the past several million years can predict aggregate climate that agrees closely with the fossil record. Projecting these models into the future reveals dire predictions for sea-level rise, large changes in habitats and farmable land, major change to sea-adjacent infrastructure, etc. The models don't vote Republican or Democrat.
There is also very little credible argument that climate modeling isn't sound science, as the basis of the scientific method is experimentation, observation, and formulation of a hypothesis that gives a predictable, verifiable outcome, and climate modeling has passed all of those tests. Because a climate model can't predict the exact temperature in your home town in two weeks (or two years) doesn't mean it's bunk or invalid, when it can very accurately predict macro-effects of the entire northern hemisphere.
I also noted here before that the Ebers-Moll model of the BJT bears only a passing resemblance to the underlying physics of doped semiconductors (it's a compromise between a first order and second order transistor model), but it's allowed countless DIY'ers to make very accurate predictions about how a BJT will function in-circuit by using SPICE. Nobody argues that the model isn't science, or that it can't be used because it isn't a perfect reproduction of the 7th order underlying physics constructs, or because there's that one oscillator that doesn't start in SPICE but works fine on the bench.
Because something has uncertainty doesn't mean the information can't be used to make accurate predictions. The GPS receiver in your car can have horrendous errors due to multi-path reflections, blocking of satellites in the sky, imprecision in sensor measurements of the cars motion, etc, but it can still place you on a road most of the time, and nobody refuses to utilize GPS because the uncertainty can be high in the raw data.