This is not true. We don’t know much about the long term side effects of either. Covid-19 is a novel virus that’s been around for approx 15 months. We have 0 longitudinal data beyond that. The same can be said of the vaccine. No side effects within a month of getting the vaccination means nothing. If significant side effects were present in the short term it would still be in the clinical trials phase.
There is nothing wrong with people picking either side as you are in the dark either way. While we can’t say anything with 100% certainty, I am fairly certain the vaccine will save many, many lives. The real question is, for those in the low risk category is the benefit in the short term worth the long term risk of what the vaccine may do. Odds are you are better off with the vaccine, but this is a free country and no one should be forced or shamed into anything.