All they have to do is throw handwavey bullshit out there until enough people doubt and do stupid made-up stuff like spacing out the vaccines for some unknown, unmeasurable benefit.
There are people in my state, in the "best country on Earth", dying from preventable diseases because of OTHER PEOPLES' pseudo-scientific crap and "beliefs". I just can't take it. When are we going to drop what we're doing and pour the billions we need into public education? - funding, reform, curriculum, emphasis on personal finance and logical reasoning skills. Pick a topic - climate change, flat earth, vaccines/autism, all of this irrationality starts with education.
Also, insurance companies go out of their way to incentivize and encourage proactive health measures, especially for younger groups; given all credible scientific research and data, and barring some other weird conspiracy, it seems reasonable to think they're encouraging vaccines because they keep people from getting preventable diseases and suffering miserable deaths.