Besides other issues mentioned, there’s likely to be legitimate variation in how people see (ostensible) ‘facts’ based on their general outlook. For example IMO some people exaggerate the accuracy problems with COVID infection and antibody tests based on socio-political outlook and ‘who is in charge’ at the highest level (it’s the wrong people in their view, therefore a tendency to view everything more pessimistically). Though it is my opinion, there are factual cases and examples of tests not accurate enough to reliably give the needed information (sometimes that’s things that were screwed up , sometimes it’s apparently just the state of the art wrt a new disease). It’s a matter or judgement if people are viewing this fairly or not. I think often not, but I’m not saying people who disagree are ‘deniers’ etc.
So likewise there could, very likely will IMO, be similar divergence in judgement about how effective a vaccine is relative to possible side effects. Different people will view different information sources which may inject their own biases as to which facts they emphasize. Again, it would be cool if these things were all a matter of some people being ‘pro science’ and others the opposite but it’s really not that simple IME.
Other thing is a pretty effective vaccine doesn’t need to be given to everybody to have a big positive effect overall. And, unlike the increasingly nakedly political fights about masks, which have little value protecting the wearer whether or not they make much difference to other people in various situations, getting a vaccine is basically to protect the person getting it. People can add on how they are also doing it to protect society because they are so noble etc., but they know the main purpose is to make their own infection less serious if it occurs. So it’s more self regulating in terms of who gets it and their outcomes. With the exception of minors, but fortunately this disease is not mainly dangerous to kids (with some serious exceptions). The usual vaccine debate is about anti-vaxxers being criticized mainly (and justifiably in my personal view) for endangering theirs and other kids.
So I’m sure everyone will not be forced to get the vaccine in a country like the US, but there probably won’t be an overwhelmingly strong rationale for that anyway.