One factor in vaccine scepticism is, as pp have said, the information which government health authorities give about vaccine campaigns and public health in general.
The aim of health campaigns is to get a population-wide response, especially with something like vaccination, because the risk to public health lessens the closer you get to a critical mass uptake.
The persuasive publicity used - as we saw in the pandemic - aims to give individuals powerful reasons to do something for the common good regardless of the extent they benefit as individuals. If authorities get it wrong, they will suffer mistrust.
And it's the case that public health information, especially in a crisis, often has the corners knocked off, it's not a complete, nuanced discussion of every issue, or the ins-and-outs of every scientific opinion. It can't be, because too many people wouldn't pay attention to the campaign, recognise the core information, or be able to take action. It's a balancing act.
PP have listed lots of contributory factors to general mistrust, even before the pandemic, such as individualisation and a growing Western sense that democratic authorities are not on the side of ordinary people. In parallel, social media provides a thousand outlets for alternative, anti-authority information, including mistrust of scientific information.
And when trust on 'the science' of one subject is lowered, it affects other areas in which scientists and campaigners are trying to engage the public, such as with climate change, green taxes, lowering emissions etc.
Which is why it's such a shame that academics, politicians, communicators and medics have been loudly telling the public, with a straight face, that humans can change sex and that sex is on a 'complicated' spectrum and that children can be born into the wrong body, while bio-scientists carefully examined their fingernails.
In the area I live in, people have become generally sceptical about government information campaigns and are becoming more inclined to 'make their own minds up' about risks.