I wonder what the threshold is. You want people to make informed decisions, but you don't want them to panic about tiny risks, because otherwise you'll get a lot less vaccinations.
Anti-vaccination is reasonable if one says "any potential side effect means I won't take it". But that seems neither individually wise nor collectively desired, though we don't really talk about the individual's responsibility as a carrier/spreader of something like influenza. Maybe we will in the future, now that it has been on everyone's mind with Covid.
On the other hand, it's hard for me to quantify the risks of the vaccines. AFAIK the only trials were performed by the companies themselves who have less than stellar track records and have no liability exposure. And while mRNA technology has been around for some time, AIUI, it's never been used en masse for vaccination purposes and we aren't really sure what to expect on longer timescales. While I suspect it's probably fine, I don't currently assign a lot of trust to public health officials due to their behavior over the past year. They've reversed their opinions/prescriptions multiple times and have proven themselves to not be above mixing politics with their health advice. It's an unfortunate reality.
My plan is to wait and see how things progress and if we get more data about both the efficacy of the vaccines and possible side-effects from more objective channels.