Your second claim is massively untrue: all of the information is public and actual medical doctors overwhelmingly support vaccination and bend over backwards trying to help patients understand it (note that most of the high profile objectors either aren't real MDs and/or are speaking far outside of their area of expertise). The problem is that many people are defining “open dialogue” as meaning that untrue statements they make need to be taken as seriously as the consensus of the scientific community.

The first is rather debatable: mandates have been highly effective everywhere they've been tried because they shift the cost calculation to “do I feel strongly enough about this that I'm willing to give up something I like?”.