Welcome back to "Doggerel," where I ramble on about words and phrases that are misused, abused, or just plain meaningless.
"Common sense" is a very nebulous term. And when it comes to science, woos find it easy to use "common sense" to reject what the evidence tells us, or to reject further analysis of a situation. The problem with this is the universe isn't necessarily what it seems to be. When you get down to tiny particles on the quantum level, well, common sense is bunk. (And no, that doesn't invalidate what science says) Our minds evolved to survive long enough to have and raise children. We have to look beyond the ego involved in assuming your intuitions and biases are infallible.
To continue with the quantum example, we don't easily understand the quantum world because we evolved in the "middle world" filled with medium-sized objects moving at medium speeds over medium periods of time. Quantum events usually go unnoticed in our world because they tend to average out. When dealing with events outside that frame, we have to resist our Newtonian biases and follow the evidence where it leads. Even if it doesn't make sense at first.
Another frame we're often stuck in is a matter of numbers. We often think in very personal terms, making us vulnerable to anecdotes. The plural of anecdote is, of course, not "data." Statistics are more abstract and impersonal, so many of us have a hard time relating. Instead, if we're, say, treated to a horror story about a child developing autism right after getting a vaccine, those who trust in the infallibility of "common sense" won't ask critical questions about timing, epidemological studies, memories biased by catastrophic, conspiratorial thinking, or ignorance of other possible explanations. In the case of autism, symptoms tend to become more noticeable around the age of vaccination, not because some eternally changing and/or unspecified "toxins" alchemically altered the child's brain. As for alternative medicine "treatments," it only takes one apparent success story to spread the good word while all the failures tend to keep quiet and just move onto other forms of woo until they get some small improvement to champion.
Common sense still has its place in the world, such as for snap judgements, and matters where little is as stake, but in a world where scientists continuously reveal deeper levels of complexity and develop better tools, scientific thinking, not gut instinct is the best method for protecting yourself. If you want to question the experts, you must approach the matter scientifically instead of spouting a collection of prejudices often called "common sense."