The general logic behind these people is that they have lost almost all faith in the main stream news. Its so bad that if you trust the news right now, then you are most likely left leaning or moderate. This culminates in a general distrust of what the news reports and now that the news is reporting that the vaccines are safe - which statistically is true - these people are tired of being lied to and are being skeptical of a quickly developed vaccine based on newer technology.

So in that population of people that distrust the news, there will be crazies that will never take the vaccine and there will be varying levels of reasonable people who decide to wait on taking the vaccine while weighing their own personal risk level with the risk of taking a quickly developed vaccine with no long term studies behind it. The longer we wait, the more of these people will decide taking the vaccine is less risky than getting covid as more studies come out, especially once the FDA promotes it from emergency approval to full authorization (which requires 6 months of data). Some of these people will of course wait longer than full authorization, they may want to wait a year or longer depending on how must they mistrust the news, its unfortunate but its going to take decades for these people to regain trust in the main stream news and the crazies I don't think will ever trust the news again.