There’s a difference between questioning the status quo and spreading obvious misinformation. Did the vaccine save lives? Yes. Did misinformation about the vaccine cost lives? Yes it did.
The fact that so much money was given to private corporations, in secret deals outside any legal proceedings, on unproven products, all while censoring any critics, really gave the conspiracy theorists water for their mill.
I believe they would have had a much harder time spreading their misinformation, if they couldn't have the street cred of having "the system" against them. That is, if we had the voice of doctors vs random loonies, instead of our respective corrupt governments vs anyone they're trying to censor.
It's typical for people in science and related fields to use carefully chosen wording, to hedge, and to speak in terms of probabilities instead of certainties.
For a general public who is used to the unashamed and unearned confidence of the usual people who get in front of a camera (politicians, celebrities, pundits) this can make it appear as though the scientific position is one with a less solid foundation, when it's usually the opposite case.
Scientific communication has been focused on insiders for so long that many communicators don't realise how it sounds to the outside world. Even the fundamental terminology is affected - a scientific theory is an overarching explanation that combines multiple pieces of evidence and creates the best synthesis we can on a topic, but to a layperson the word theory means "vague idea".