This is a bit of a misnomer, that it is such a new vaccine that was never tested for long periods of time. The mRNA form of vaccine has been in research and testing for decades already. Not specifically for covid of course but they have been working with this technology for quite a while.
I did read an article yesterday about side effects of vaccines and it said that historically when vaccines have had serious side effects that they have nearly always shown up relatively quickly, 2 months IIRC. So if you wait for at least two months on these new vaccines and they haven't found serious side effects then the risk of later side effects would seem to be quite low.
The whole argument of "unknown side effects" skeptical of vaccines always bring up but they are really a double edged sword. While they don't know the side effects of the vaccine 5-10 years from now, they also don't know the side effects 5-10 years after having covid either.
The problem with THIS vaccine family is that you CAN'T draw similarities regarding side effects to vaccines of the past. "that it is such a new vaccine" negates your historical reference -- that serious side effects have nearly always shown up relatively quickly, (2 months). Since those vaccines were derived most often from organic sources, such as the living or dead viruses themselves, and this new family of vaccines changes the body's DNA to generate the required antibodies is enough to say we are sailing in uncharted waters.
If the technology and research have been around for years, and there have been no previous vaccines used for other diseases, why would we think this is something we should embrace 100%? I think it was great that Operation Warp Speed produced a CANDIDATE vaccine so quickly, but that vaccine should also be tested and studied just as much as any other vaccine -- probably more so -- precisely because it IS a technologically new vaccine for a new virus.
I can't believe drugs we have known to be safe for many decades -- like anti-malarial drugs -- were scoffed at as irresponsible and "not scientific," yet a mostly untested vaccine based on new technology for a perviously unknown disease should be shot into 100% of peoples' arms without delay.