I doubt people who want the vaccine are now going to change their mind based on what one doctor on the news says.
Let the anti-vaccine people use the clip to their hearts content if that’s what they want to do to validate their opinions, but it won’t have any bearing on the people who know the importance of getting vaccinated and want to do so.
After all, it’s not as though he’s telling other people not to get vaccinated, he’s just saying that in his own circumstances he doesn’t feel he needs it.
Just because the doctor doesn’t agree that vaccines are necessary for him personally, that doesn’t mean he should be silenced. It’s called freedom of speech.