Note that all of your examples have experts on all sides of the argument. If evidence doesn't matter, then there's enough expert testimony to back that cigarettes aren't harmful for your health and that vaccines cause autism. Because experts.
Your example disagreements have definite conclusions, because there was copious evidence supporting one side of the argument. For example, there was a three orders of magnitude drop in US measles cases right after the introduction of the measles vaccine. And similar drops can be seen in other countries as respective vaccines are introduced. And the side effects of these diseases can be just as dire as autism, the alleged side effect of vaccination. There is a very straightforward argument to be made for continuing vaccination, even if it did cause autism due to the people whose lives are saved from these diseases.
Similarly, there is very strong evidence over large numbers of people that smoking harms people, both the smokers and people who are exposed to high levels of second hand smoke.
The special features of these debates is that one doesn't need to listen to the experts. One can study the evidence directly.
What I think is dishonest here is the assertion that the evidence for the claims of catastrophic anthropogenic global warming (CAGW) is just as strong as the two examples you gave and just as easy to examine to confirm. It isn't. After all, we don't measure directly any weather or climate phenomena before about 150 years ago. Every is estimated via paleoclimate proxies. And these estimates are very subjective, dependent on how they are manipulated. For example, the first reconstruction of global mean temperature over the past millenium which eliminated the Medieval Warm Period, the "Hockey Stick", by Mann and Jones, turned out to have a serious statistical error, which conveniently caused even random noise to be transformed to the desired "hockey stick" shape, most of the millennium being nearly flat except for a sharp rise in temperature at the end in the Industrial Age. What is particularly interesting is that after this research was called into question, within a few years, supposedly independent research had been released showing the same shape.
Where else in science, would scientists work so hard to recover a broken result? I'd say economics which has long been held captive by a variety of special interests. In most fields, bad research would be a warning sign to look hard at the problem and carefully reevaluate the original claim, rather than rush through new analyses to back the original claim.
And then we have the second tenuous claim, that it is catastrophic. The evidence for this is laughable. A particular notorious example are the claims of extreme weather. They come in two variants. The first are claims that various special cases of weather are due to global warming. These are inherently dishonest both because it is nearly impossible to show that any single incident of weather was made worse by global warming. One shows correlation by looking at lots of data. Even the instrument period of the past 150 years often doesn't have enough data to back these claims.
The second approach is to study the models and make predictions from those, though not couched as such. So it is claimed that say, tornadoes are 33% stronger in terms of damage inflicted than they used to be, or there are more hurricanes, when what is really meant is that the researcher is extrapolating from a model, rather than reality, and no one has a clue yet whether the hypothesized effect occurs because the necessary data isn't yet present.
My view is that in climate research, we have a real life demonstration that experts are not evidence.
