That's almost a straw-man argument. When you're making statements about pure probabilities, everyone is a bayesian. Most toy examples make "frequentists" look like morons, because essentially all of the judgement and discretion is removed from the problem, so you'd have to be an idiot not to apply Bayes's rule.

The difference shows up when you actually have an interesting data set to analyze. Bayesian statistics can disagree with frequentist stats in small samples because they're (often) using different normalization strategies; and they can disagree in large samples where the CLT fails. There may be other settings where they diverge too that I'm not aware of. But neither of those scenarios is one where insisting "I'm a Bayesian, so the answer is blah" or "I'm a frequentist, so... blah blah" is likely to be a good strategy. Those are the settings where it's hard.