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 "that it is such a new vaccine" negates your historical reference -- that serious side effects have nearly always shown up relatively quickly, (2 months).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.
You may be right, that you can't compare side effects of old styles of vaccines to side effects of this newer style of vaccine. I haven't come across whether there is reason to believe this new form of vaccine will behave differently in terms of side effects than more traditional methods. However i do think that since they have been researching this new technology for about 30 years they they probably have at least some idea of what to expect in terms of side effects. It had been tested on people as well as dogs IIRC well before the covid one was developed. That being said I can definitely understand people's uneasiness of trying this new technology.
I watched a good video today where a doctor was explaining the expedited process of vaccines and it isn't as bad as it sounds. There is a lot of red tape in the FDA and things often take time due to the bureaucracy. not just because of how long trials take. Additionally the government's promise to pay for the vaccines enabled companies to dive in much quicker since they didn't have to bear the financial risk of making a drug that might not end up panning out. I don't know that any of the actual trials were rushed in terms of how long test subjects were observed or whether they were done faster than usual but I know clearing the red tape was part of the quicker than usual approval.