The thing is, for every one drug that's mentioned as bad (from the 50's), there's 100 that are good, and a 1000 since that have been even better. The "bad" 1 might injure or even kill 100 (yet still probably saves 10x that), the 100 good might save or help 1 million (with little side effects), the extra thousand might save 100 million (with barely any side effects). All of the "bad" ones, mean we have become more regulated and learnt more from previous mistakes, so previous failings, realisations and corrections, are probably more a reason to trust medical science now. It's the same for technology, cars, computers, phones etc, things start off ok, then get good, then great, and then ridiculous.
They need to look at it relatively and compare it to the alternative. There is no alternative where they choose not to get vaccinated, then go to the pub every Friday and Saturday and don't get exposed to covid. It's a vaccine reducing risk by 95% for most adults, or they face a risk 20x more by not getting vaccinated.
Those making, regulating, approving and carrying out the vaccine injections understand more than those saying "we don't understand them", in reality, those not having them, are the only ones that don't understand them, and certainly don't know how to compare relative risks of vaccination and covid, never mind factoring in for reciprocal and economical benefits from having this under control faster.
We might have been at 0.1% of possible knowledge in the 1900's, then 1% in 1950, now we might be at 50% and in 30 years that may be 90%.
Comparative risk in 1900 might have been 50%, then in 1950 20%, now 1% and in 2050 0.1%.
Either way, comparing now, to limited issues 70 years ago, and using that as a reason to not do something now doesn't make any sense, never mind factoring in now that things are more regulated and better known than at any point in history.
The probability of errors is not massive, it's tiny, and even less compared to what it's saving, and the probability of errors, will only decrease.
There is no time to wait 20 years to realise the short, mid, and long term effects of vaccination are safer, as by then 100 million could have died, and we already know covid kills 1% without treatment/ vaccines, and that's without healthcare overwhelmed.
You don't not put on a parachute, because there's a better model parachute coming out in 20 years, or you don't wait 10 years to see if that first one would have worked when every skydiver is telling you to just use it.