My wife and I are dealing with this as new parents. Even setting aside the COVID vaccine which looks completely unnecessary for infants, there were a ton of other issues that lost our trust. The CDC does not for example recommend aspirating the needle anymore during shots because "there are no large blood vessels" (this is wrong - anatomy has outliers, and anyway there are smaller ones) and it "might be more painful for infants" (this is a not a good reason). This shocked our doctor who said they always aspirate and were trained to do so. We had our pediatrician aspirate and it took less than a second. I could write more about why we insisted on aspirating but that's another can of worms to make the same point which is you can't take CDC at its word. We are scrutinizing every advice and every vaccine whether the benefits (individually and to society) outweigh the risks. So far I think we probably will end up doing the main ones, but we're doing it our way, on our schedule, and specifically choosing vaccines with certain ingredients to minimize risks. We know other parents that are opting out completely and I can't blame them. It would be easier if we could just trust the CDC.
No, politicizing vaccination is breaking trust in vaccination. Social media is breaking trust in vaccination. None of the things we vaccinate against are harmful until they are. Society is a group activity and operates best when there is shared responsibility for its success. Something that minimizes your risks along with the risk of others is an example of the glue holding things together.