If the inferential question you're interested in is, "given data X, what do I conclude about underlying cause/variable/parameter T?", then you are a Bayesian, l

If the inferential question you're interested in is, "given data X, what do I conclude about underlying cause/variable/parameter T?", then you are a Bayesian, like it or not.* Sure you can define a likelihood function p(X|T), but that doesn't give you p(T|X) unless you multiply by a prior p(T). Now certainly p(T|X) is not always the question, but in the vast majority of cases people do want to use data to draw conclusions, and will misinterpret likelihood-based confidence intervals as posterior credible intervals because the latter are what they intuitively wanted. By doing so they implicitly assume a flat prior regardless of whether that that is reasonable or even mathematically coherent for the problem in question. The Bayesian argument is not that you have to use an informative prior (though often this can be very helpful!), but that since some sort of prior is mathematically necessary to answer the questions that people intuitively want statistics to answer, we should make that explicit and try to understand how the prior affects our conclusions, not just sweep it under the rug. * If the question you're interested in is, "if I run some method in many repeated trials, how often will it identify the true parameter?" then you are a frequentist. I think it's much rarer for this to genuinely be someone's intuitive question, but it's certainly valid. And of course it's valid to ask both questions at once, in which case you might end up analyzing the frequentist properties of a Bayes-derived method.