Nearly every medication will affect some people adversely. This can be due to allergic reactions or other existing conditions (including congenital ones). This is why so many drug commercials have a disclaimer with all of the possible negative side effects. Think of how many of these often include death as a "side effect.''
Rushing out a vaccine to deal with a highly-contagious infection that has a relatively high mortality rate increases the likelihood that there will be adverse reactions, including death. The extent of the rollout also leaves us without an answer to the question of what would have happened otherwise. Lots of people died from COVID. Some may have died from the vaccine. The lack of certainty is where conspiracy theories get their momentum.
We had some people here who appeared to have bought into the idea that COVID and the vaccines were part of a conspiracy to drastically reduce the world's population by killing off billions of people. Time has shown that to be... mistaken. It may be decades more before we learn enough to know just how bad COVID was, and how bad the vaccines were/weren't. Until then, enjoy the conspiracy theories.