The science on vaccines is solid, but there are potential side effects (that's also solid science). So when it comes to, for example, giving kids the vaccines, we have to balance the likelihood of serious side effects with the necessity of preventing the disease. In the case of COVID, the disease's risk to kids is extremely low, but they are still vaccinated. That is a political decision, and it is perfectly reasonable to dispute it.

That's a particularly clear cut example. There are many more complex scenarios where "trust the scientific experts" is dubious because science has a limited domain of applicability. When you pretend that non-scientific decisions must be made on a scientific basis, people see through it and become sceptical.