Sarah Zhang in The Atlantic:

mRNA vaccines are similarly new, but they have so far racked up a good safety record. So many doses have been administered that these unusual blood clots—or any serious one-in-a-million event—would very likely have shown up by now. Back in December, experts quickly noticed and warned the public about a handful of severe allergic reactions to the Pfizer-BioNTech and Moderna vaccines, which is why vaccination sites now monitor recipients for 15 to 30 minutes after the jab.

At the end of the day - its is all about managing risks. The Pfizer-BioNTech and Moderna vaccines have both demonstrated 100% effectiveness preventing serious disease and hospitalizations. Just get vaccinated!