Bayesian and frequentist results are not the same, ever

I often hear people say that the results from Bayesian methods are the same as the results from frequentist methods, at least under certain conditions. And sometimes it even comes from people who understand Bayesian methods. Today I saw this tweet from Julia Rohrer: "Running a Bayesian multi-membership multi-level probit model with a custom function to generate average marginal effects only to find that the estimate is precisely the same as the one generated by linear regression with dummy-coded group membership." Which elicited what I interpret as good-natured teasing, like this tweet from Daniël Lakens: "I always love it when people realize that the main difference between a frequentist and Bayesian analysis is that for the latter approach you first need to wait 24 hours for the results." Ok, that's funny, but there is a serious point here I want to respond to because both of these comments are based on the premise that we can compare the results from Bayesian and frequentist methods.