The establishment has done very little to try and address concerns from vaccine skeptics. Their response is mostly one of condescension and derision. Rather than using kindness and education, many establishment folks simply refuse to meet these people where they are and instead continue to act as though it’s completely insane to question the things that are being injected into their children.
There are completely valid questions for normal people to ask that don’t receive much of a response often, things like “why are vaccines immune from lawsuits?” and “why has the standard vaccine schedule increased so much?”.
Instead of providing good clear answers to these questions, skeptics are marginalized. How can this behavior not create distrust in scientific experts? The more you talk down to people, the less likely they are to trust you.
Note: I myself am not a vaccine skeptic, but I know many and I hear their reasoning often.