When confronting conspiracies, the most important thing you can do is ask questions. The conspiracy theory falls apart on its own thanks to internal inconsistencies and logistical impossibilities.
Ask questions like: Who are 'they'? What is their objective? How do they benefit? How many of them are there? Who needs to be 'in on it'? How do they recruit the person who does x? How do they keep even a single person from squealing?
People who believe that vaccines are part of a conspiracy to "control" people (whatever that means), generally also believe the vaccines are harmful, but this is logically inconsistent. If "they" desire a population that can be "controlled", then wouldn't they want the people who are most compliant to have the highest rate of survival? Therefore, the vaccine would have to be very safe and highly effective at preventing disease.
These goals are aligned with the normal universe so the "control" narrative is really meaningless in the context of vaccines. If the conspiracy theorists really wanted to disrupt the powerful conspirators ability to control the population, they should ensure that the resistors are vaccinated in the highest numbers!