In my laboratory statistics manual from college (the first edition of this book) the only statistics were frequentist, and Jaynes was considered a statistical outlier in my first year of graduate school. His results were respected, but the consensus was that he got them in spite of his unorthodox reduction method, not because of it.

In my narrow field (reflection seismology) two of the leaders explicitly addressed this question in a (surprisingly to me little-read and seldom-referenced) paper: To Bayes or not to Bayes. Their conclusion: they prefer their problems neat enough to not require the often-indispensable Bayes method.

It is a debate I prefer to avoid unless it is required. The direction of progress is unambiguous but it seems to me a classic example of a Kuhn paradigm shift where a bunch of old guys have to die before we can proceed amicably.

A very small minority of people hate Bayesian data reduction. A very small minority of people hate frequentist data reduction. The vast majority of people do not care very much unless the extremists are loudly debating and drowning out all other topics.