The vaccine doctor guy, Paul Offit, MD, in one of his many books about vaccines (they are all very good reads), tells a story of a man in the UK who took his infant son to be vaccinated, stood in line for a while, but decided he couldn’t wait any longer, and went home without the shot (IIRC, DTaP). The baby died of SIDS that night.
Offit comments that had the man stayed in line and gotten the shot, there is no way you ever could have convinced the man that the vaccine did not kill his son.
There’s also a couple on a crusade against the hep B vaccine for infants, because they lost a newborn who was give the vaccine. Nevermind the infant was in special care, and recovering from a reaction to an antibiotic, when he was accidentally given another antibiotic in the same class. The antibiotic was closer in time to the death than the hep B vaccine, but the parents were already vaccine skeptics who felt they had been pressured into allowing the vaccine.
As much as I hate it, I think in the long run, more people will get vaccinated, if the AZ vaccine is approached with caution. It will probably be allowed eventually, but maybe at first not given to people with previous clotting events, or other reasons to think clotting could be a problem.
There are anti-vaxxers who are not going to get vaccinated no matter what, but they are the minority. There are lots of people who are concerned or hesitant, who will feel better if their concerns are taken seriously. Some kind of trial specifically to look at the issue may put a lot of people at ease.