But simply ignoring or minimizing the risks of that the limited testing on the vaccine is a dishonest way to present the situation.
Can you expand on your point about limited testing? My understanding is that the vaccines have all been through every traditional trial stage. The vaccine has only been "rushed" in the sense that the other, more bureaucratic steps have been minimized.
Since so much money has been shoveled into this problem, companies have not had to take time to raise money. They were able to examine multiple leads at once, rather than sequentially. They have built on previously tested vaccine mechanisms, only switching out the particular genetic material for this virus. They were allowed to start the next trial phases before all the previous ones were finalized, but not before preliminary data came in (and the early trials were still continued to make sure nothing unexpected came up). It took no time to recruit volunteers for the trials, and covid is so rampant now it didn't take as long as usual for a critical mass of trial volunteers to contract the disease and allow for the data analysis. And, of course, much of the FDA red tape has been minimized.
That's not to say that it's impossible for longer-term or more rare effects to arise in the future, but that is true of every vaccine introduced to the market that has undergone the same trial stages with the same number of participants. Some things just aren't going to show up until you have the numbers of the general public involved. But the vaccine has undergone the same level of testing as every other vaccine. The corners haven't been cut in the science, just in all the other barriers.
I admittedly have the perspective of a young, healthy person who had covid in March, is still dealing with lung issues when I exercise, and would have happily volunteered in a vaccine trial if my prior covid case weren't disqualifying. So perhaps I just have a different risk analysis.