Well, consider that a lot of people who aren't applying as much caution to the virus itself just don't think it's that big a deal. Either they think their infection risk is low, or they expect they'll be asymptomatic, or think that even symptomatic infections aren't that bad. Through that lens, it makes sense to be wary of taking a vaccine with possibly-dangerous side effects when they don't believe the virus it protects against is all that bad.

I don't agree with the premise behind this reasoning, but I can see how it'd come about.