As a nature-loving physical therapist in Boulder, Colo., Colin O’Banion shops at farmers markets, grows organic squash in his backyard and thought he could never vote for Donald J. Trump.But during the pandemic, he said, he and his wife became social outcasts when they refused Covid-19 vaccines for themselves and their three sons. Tuning in to alternative health podcasts, he became convinced that the country’s public health establishment was corrupt, and that the only antidote was the upheaval being promised by Robert F. Kennedy Jr. as he teamed up with Mr. Trump. “That’s what brought me on board,” Mr. O’Banion,...