This is why no one trusts "institutions" anymore. The researches finding out if vaccines are dangerous should be focused on that single thing, not worried about how the results might be interpreted. In my opinion, THAT is what undermines trust.
The more bad faith discourse dominates, the more cautious and defensive institutions get. The more defensive institutions get, the more bad faith discourse dominates. If institutions apologize for having been wrong or lied in the past, that will only be used to strengthen the anti-institutional narrative. If they don't apologize, that will only be used to strengthen the anti-institutional narrative. There is no way out. We are in a death spiral.
I guarantee this paper is going to instantly make the rounds in anti-vaxx camps and will be used to imply that vaccines cause everything from autism to the common cold. That will only cause researchers to be even more hesitant to publish anything actually concerning about vaccines, since they'll know that any doubt will be weaponized. That in turn will make people even more distrustful and more likely to trust quacks, ideologues, and lurid tabloid-style material.