To be a reasonable concern it has to be weighed against the alternatives. People have essentially four options assuming the virus does't just go away soon: get vaccinated using a new technology, wait for an older technology vaccine to be available, mask/isolate until the new vaccines have sufficient long-term data for their ill-defined concerns, get COVID.
Well COVID has high risk for long-term effects for all age-groups including death so any reasonable person will exclude that option. Older technology vaccines for many regions of the world may never be available or be sufficiently efficacious so that and masking/isolating indefinitely and maybe even getting COVID are the same option. Plus, there is no data showing any long-term effects for vaccines that don't become apparent in the first year or 100 million people receiving them.
COVID vaccine hesitancy is no longer a reasonable position to hold.