From a public policy standpoint they are safe and effective. There really is no disputing that. We are talking over 10 BILLION doses across 70% of the human population. If they were not safe and effective society would have completely collapsed. It would be Mad Max.
I think the scale is very confusing. It's hard to think in the billions. At this scale the amount of adverse reactions will reach into the millions, but you are still looking at a very small probability. 1%, 0.1%, 0.001%, 0.0001% all get muddled up in people's minds. If you have no training in statistics these often "feel" like the same numbers.
The average lifetime risk of dying in a car accident is 1 in 100. You probably know someone whose died in a car accident. If you think about long enough, you know multiple people. You (probably) still drive. With "the vaccine" we talk about adverse reactions in the millions. Often single digits. One in a million. Five in a million. 10 in a million. In some cases you may even get into three digits! 100 or 200 per million. But even 1,000 in a million reduces to 1 in 1,000. Even if you stretch it out to something ridiculous like that you still end up an order of magnitude less than the kind of risks people generally consider safe.