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@Karthikdeva
I like that you said Belief System, which everyone has, whether they (or you) describe themselves as Religious.
I think the question also comes down to : what do you mean by "science" that one can reject? Does it mean methods, popular opinion on conclusions (consensus) or simple a competing Belief System?
@SecondJon There are two types I believe,
1, A person directly contradicting a scientific fact and chooses to ignore the said fact to cater/nurture their belief system.
2. When no valid argumentation is discovered for a subject yet, the masses resort to pseudoscience.
Some examples which advocate someone rejecting science over their 'belief' systems are anti-vaxxing, flat-earth theory, Neo-creationism, Holocaust denial, etc. (
So what I mean by science is 'Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe.' (definition from Wikipedia)