This is a parallel to the Observer Effect (which is not apparently the same as Heisenberg's Uncertainty Principle). https://en.wikipedia.org/wiki/Observer_effect_(physics)

If you could "do everything right" you couldn't at the same time "manage a real time communications challenge" given how hostile the environment is tp rational inquiry. The time you spent managing communications would be interpreted by those who irrationally question the validity of your inquiry as a validation of their (for lack of a more objective term) paranoia.

Whatever energy you spend in fact-checking the irrational behavior of anti-vaxxers will be interpreted by the anti-vaxxers as a validation of their "belief" in the flaws of your premise.

It's a Chinese finger pull. The real loser isn't the CDC but the people who are trying to minimize transmission of COVID 19 by wearing masks, social distancing, getting vaccination shots, etc.

From what I've read, the Delta variant may mutate so that a significant number of vaccinated individuals will be infected. Delta will achieve immunity from the vaccine because of those who refuse to be vaccinated. And there's apparently nothing the CDC (or anyone else) can do or say to convince the anti-vaxxers otherwise.