What sets science apart from most other methods of seeking answers is its focus on disproof. Your goal as a scientist is to devise experiments that can disprove a claim about the natural world.
This misconception rears its head most prominently in discussions at the intersection between science and public policy. Climate change. How to handle a pandemic. Evolution. Abortion. But I've even talked to scientists themselves who from time to time get confused about what science can and can't do.
The problem with believing that science proves things is that it blinds its adherents to new evidence paving the way to better explanations. It also leads to the absurd conclusion that a scientific question can ever really be "settled."
It is simply wrong to think that scientific questions can never be definitively settled. Clearly there are some hypotheses that have been difficult (and may be impossible) to prove, for example, Darwin's idea that natural selection is the basis of evolution. There's ample correlative evidence in support of natural selection, but little of the causal data necessary for "proof" (until perhaps recently). In the case of evolution the experiments required to prove that natural selection could lead to systematic genetic change were technically challenging for a variety of reasons.
In the case of climate change, the problem again is that the evidence is correlative and not causal. Demonstrating a causal link between human behavior or CO2 levels and climate change (the gold standard for "proof") is technically challenging, so we are forced to rely on correlations, which is the next best thing. But, you are right, it is not "proof".
Establishing causality can be difficult but not impossible - the standard is "necessary and sufficient". You must show necessity: CO2 increase (for example) is necessary for global warming; if CO2 remains constant, no matter what else happens to the system global temperatures remain constant. And you must also demonstrate sufficiency: temperatures will increase if you increase CO2 while holding everything else constant. Those are experiments that can't be done. As a result, we are forced to rely on correlation - the historical correlation between CO2 and temperature change is compelling evidence that CO2 increases cause global warming, but it is not proof. It then becomes a statistical argument, giving room for some to argue the question remains "unsettled".
My point is that there are plenty of examples in science where things have been proven -- DNA carries genetic information, DNA (usually) has a double stranded helical structure, V=IR, F=Ma, etc. And there are things that are highly likely, but not "proven", e.g., human activity causes of climate change.
While some of the issues you bring are remain unproven, what's really absurd is to think that no scientific questions can be settled.
This is not mutually exclusive with being against the attacks on science. Just because we shouldn't treat things as proven doesn't mean we can't come to a general consensus on a topic and act as if it was true. Climate change is real. Evolution is real. Don't inject yourself with bleach. Having a small number of quacks say 'its just a hypothesis and actually god is responsible for climate change and evolution' without any evidence doesn't change the general consensus and doesn't mean we have stop everything until we prove the negative.
Ultimate I think most of us agree in principle. Most of what we're discussing here is minor semantic differences in vocabulary.