It's not common enough to prevent herd immunity.
Motadel 4-29-2021. [David, Ph.D., Associate Professor, International History, London School of Economics and Political Science; “Vaccine Hesitancy Is as Old as Vaccines. I Take Comfort in That,” New York Times, https://www.nytimes.com/2021/04/28/opinion/vaccine-hesitancy-smallpox.html //cpsw-ay]
Throughout history, critics of vaccines have argued that immunization is more dangerous than disease itself. They have claimed that there are malicious, nonmedical reasons behind vaccinations, such as the profiteering of Big Pharma and biological schemes intended to reduce the human population. And they have been driven by exquisitely complex and diverse reasons: uncertainty, fear, science skepticism, anti-intellectualism and anti-elitism; sometimes they are motivated by profit.
But although attempts to delegitimize vaccines have posed a serious threat to human health, anti-vaccination movements, at least in the long run, have never succeeded in stopping rollouts. The spread of medical information, which took away most people's fear of the unknown, as well as the actual experience of the successes of vaccinations, have made populations increasingly less receptive to anti-vaccination messaging -- even as communicating those messages has gotten easier.
To put it another way, enough people have accepted vaccines that they have always been effective in immunizing societies. And that's likely to be true of this pandemic, too.