It's real. I don't know about O'Reilly, but Trump was vaccinated before he left office. He doesn't talk about it publicly very much, but he did speak at a rally back in August, and recommended vaccinations.
The audience booed then, too.
https://www.nbcnews.com/politics/donald-trump/trump-booed-al... https://www.foxnews.com/politics/trump-targets-biden-over-af...
The new news is that he also got a booster, and got booed again.