mRNA's short half-life - on the matter of a few dozens of minutes - and pre-existence in our bodies helps us not worry too much about the differences in delivery mechanism.
"We think based on biochemistry that mRNA acts like this, and we hope it does that, and we think it probably does the other" doesn't carry much weight here. The probability of any element of that chain of logic being wrong is too high.
I'm not saying that testing wasn't done. I'm saying "eh, it's probably OK, mRNA looks pretty safe" is not a useful contribution to this sort of discussion.
Barring a time machine, the "is it safe ten years from now" cannot be answered conclusively today. We're left to use other available evidence to make a risk analysis, like "mucking with the immune system tends to have effects that show up fast" and "what do we know about mRNA in the body, especially when delivered by viruses?". There's a risk to inaction, too.
We don't look at evolution and go "welp, can't test evolving humans from microbes, so we must avoid drawing any conclusions".
So go get vaccinated! If you trust the vaccine that it works, and that it's safe, go get it. I certainly have urged people I know who are high-at-risk and don't share my ethical concerns about them to get the vaccine.
If they're safe and effective, get vaccinated!
If they're safe and not effective, or lossy effective, we have very big problems and vaccinating the hold outs will not change anything