Fast doesn't mean rushed. The trials were fast because it was easy to gather huge numbers of participants, and the phases were carried out in parallel rather than sequentially (normally, to save money/resources, phase II would only start after a successful phase I).
> and pressured approvals
Immense pressure to make sure it's safe, too. Like this precautionary pause for what seems like a lower blood-clot rate than would be expected just by chance in that size of population.
> but many people who are wary are often put in a corner of conspiracy theorists and I don't think this is fair.
I think think this happens for at least two reasons. First, they are often simply conspiracy theorists who just try to phrase their thoughts in a way that doesn't seem like conspiracy theory at first. I've talked to a lot of people (mostly online) and I can tell you that it happens a lot. And the same people will start the same conversations again and again along the same patterns, pretending they are not conspiracy theorists or anti-vaxxers for that matter but go down the same path and show themselves if you engage in a discussion.
Second, because of the above phenomenon, some people will just jump to the conclusion that anyone who raises concerns are indeed conspiracy theorists. (Again, because a lot of them will pretend that they are indeed sane people having sane questions.) It's not ideal, but not surprising either.
Fun fact: thalidomide, the drug that caused birth defects, would have passed the trials that the Moderna vaccine's been though, because pregnant women weren't included in the study participants.
Next to that: Over the last 50-60 years approved medicines with the backing of more extensive clinical trials have been withdrawn. So the whole process in itself isn't flawless.
I'm not saying the vaccines are unsafe or all the processes are wrong, but many people who are wary are often put in a corner of conspiracy theorists and I don't think this is fair.