That isn't why there's a frequentist/Bayesian dispute. Everyone agrees they are both "interpretations". As another commenter has pointed out, the semantic argument is just a proxy for the dispute over whether one or other interpretation is preferable either philosophically or in practical terms.

Calling them interpretations seems to imply that at most one of them can be correct. "Displacement of a falling object on earth" and "kinetic energy of an 18.6 kg object" aren't competing interpretations of the math f(x) = 9.8x^2, they're just two different things the equation applies to.

If the frequentists are making any error, it's denying that beliefs must be updated according to the Kolmogorov Axioms, not asserting that frequencies can also be treated with the same laws. It's denying the former that might lead them to apply incorrect methods in inference, which is the only problem that really matters.