I came across this sally in the Bayesian/frequentist wars:
In general, the religious Bayesian states that no good and only harm can come from randomized experiments. In principle, he is opposed even to random sampling in opinion polling. However, this principle puts him in untenable computational positions, and a pragmatic Bayesian will often ignore what seems useless design information if there are no obvious quirks in a randomly selected sample.
— Herman Chernoff, Sequential Analysis and Optimal Design, Philadelphia : SIAM, 1972
This doesn’t seem to capture the current state of things, but the upshot here is that Chernoff is calling shenanigans on the “philosophical consistency” of Bayesian statistics.
Sometimes I wonder if what is needed is a Kinsey scale for statistical practice… can one be Bayes-curious?