I’m still convinced that Americans tend to dislike the frequentist view because it requires a stronger background in mathematics.
I think it’s useful to break down the anti-Bayesians into statisticians and non-statistician scientists.
The former are mathematically savvy enough to understand bayes but object on philosophical grounds; the later don’t care about the philosophy so much as they feel like an attack on frequentism is an attack on their previous research and they take it personally
There are some cases, that do arise in practice, where you can’t impose a prior, and/or where the “Dutch book” arguments to justify Bayesian decisions don’t apply.
The p-hacking exposures of the 1990s only fermented the notion that it is very easy to get away with junk science using frequentest methods to unjustly validate your claims.
That said, frequentists are still the default statistics in social sciences, which ironically is where the damage was the worst.
But I think the crux of the matter is that bad science has been demonstrated with frequentists and is now a part of our history. So people must either find a way to fix the frequentist approaches or throw it out for something different. Bayesian statistics is that something different.
The first statement assumes that parameters (i.e. a state of nature) are random variables. That's the Bayesan approach. The second statement assumes that parameters are fixed values, not random, but unknown. That's the frequentist approach.
But what I gathered after moving to Seattle is that Bayesian statistics are a lot more trendy (accepted even) here west of the ocean. Frequentists is very much the default, especially in hypothesis testing, so you are not wrong. However I’m seeing a lot more Bayesian advocacy over here than I did back in Iceland. So I’m not sure my parent is wrong either, that Americans tend to dislike frequentist methods, at least more than Europeans do.
To read this book will be much better, then to apply "Hanlon's Razor"[2] because you see no other explanation.
In reality, on a human level, it doesn't work like that because, when you have disagreements on the very foundations of your field, although both camps can agree that their results do follow, the fact that their results (and thus terminology) are incompatible makes it too difficult to research both at the same time. This basically means, practically speaking, you need to be familiar with both, but definitely specialize in one. Which creates hubs of different sorts of math/stats/cs departments etc.
If you're, for example, working on constructive analysis, you'll have to spend tremendous amount of energy on understanding contemporary techniques like localization etc just to work around a basic logical axiom, which is likely irrelevant to a lot of applications. Really, this is like trying to understand the mathematical properties of binary arithmetic (Z/2Z) but day-to-day studying group theory in general. Well, sure Z/2Z is a group, but really you're simply interested in a single, tiny, finite abelian group, but now you need to do a whole bunch of work on non-abelian groups, infinite groups, non-cyclic groups etc just to ignore all those facts.
I’m not following your exemple about binary and group theory either. Nobody looks at the properties of binary and stops there. If you are interested in number theory, group theory will be a useful part of your toolbox for sure.
To understand both camps I summarize like this.
Frequentist statistics has very sound theory but is misapplied by using many heuristics, rule of thumbs and prepared tables. It's very easy to use any method and hack the p-value away to get statistically significant results.
Bayesian statistics has an interesting premise and inference methods, but until recently with the advancements of computing power, it was near impossible to do simulations to validate the complex distributions used, the goodness of fit and so on. And even in the current year, some bayesian statisticians don't question the priors and iterate on their research.
I recommend using methods both whenever it's convenient and fits the problem at hand.
Regardless, the idea that frequentist stats requires a stronger background in mathematics is just flat out silly though, not even sure what you mean by that.
There is a reason why conjugate priors were a thing.
The opposite is true. Bayesian approaches require more mathematics. The Bayesian approach is perhaps more similar to PDE where problems are so difficult that the only way we can currently solve them is with numerical methods.