From what I have read of the comments by those who are anti-vaxers, climate change deniers, and who think smoking tobacco is not a health hazard, their mindset regarding those ideas (including the way they determine what information sources are reliable) and the way they spread their views are like those of young earth creationists (and others who reject that biological evolution is a fact), people in religious cults, people who believe space aliens have visited Earth and abducted humans, people who denigrate science (even referring to it as a cult), and people with far 'right'-wing ultraconservative political views.
It has been more than 4 months since I took my first Covid-19 mRNA based vaccine dose and according to a number of blog/forum posts by anti-Covid-19 vaxers I should be dead by now or at least in horrible health. Yet, here I am with still excellent health (including normal blood pressure, normal heart rate, normal respiration, and normal healthy body weight) despite being over age 50. About 85-90% of the people at my place of work (of about 500 people) are fully vaccinated from Covid-19, but according to many blog posts by anti-Covid-19 vaxers they should all be dead now or in terrible health as a result of the vaccine, yet the vaccine has not caused them any harm (at least none that anyone knows about). Likewise my sister and my elderly mother took the same Covid-19 vaccine as I did and they tell me they have not detected any adverse health effects from the vaccine (other than the initial soreness at the vaccine injection site).
Having a doctorate in philosophy is helpful in knowing how to evaluate competing claims, to think critically, and to think logically. Courses in logic and critical thinking are courses of philosophy departments at universities. At university I took two philosophy courses in logic and one of those two also taught critical thinking. The philosophy department also has a course in philosophy of science. I didn't take that course, but about 2 years ago I purchased a book on that subject and read it. Prior to about the year 1900 or 1800 science was known as natural philosophy and was thus a branch of philosophy.