What examples have you come across where a person or group was unable to accept flaws in a theory because they have already built the theory into their mental model of the world?
For example, some economists do not accept evidence of the 'low-volatility anomaly' because of their belief in the efficient market hypothesis.
At the theology end of the spectrum, theories can be incredibly flawed (in the sense of being terrible predictors of experimental outcomes) and still attract new believers.
At the physics end of the spectrum, while the best theories are slightly flawed, they work well enough that rational people choose to build a worldview around them rather than throw up their hands in despair.
The low-volatility anomaly is more like the physics end of the spectrum. Empirical data doesn't quite match the theory, but nobody has a definitively better theory. Economics is the study of rational actors, but some actors are irrational, so results will never match the real world exactly.
(The low-volatility anomaly is partly a principal-agent problem: the principal has a rational risk/return tradeoff, but brokers rack up more fees with high-risk hedging strategies.)
Like when I asked my first-grader what's 4+5 and she said "6?", that doesn't shake my belief in the theory of arithmetic.