Bayesianism is applied Bayesian probability theory. Bayesian probability theory is math. Which of those two propositions do you disagree with?
Frequentists accept all of the math behind Bayes Theorem, but are not Bayesians. The interpretation of probability is a philosophical subject, not something that is a straightforward consequence of the math.
Bayesianism is applied Bayesian probability theory.
Bayesianism is applied probability theory with additional epistemological premises. You can accept the former while rejecting the latter.
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