Every response to question in this thread that I've seen so far is overly wishy washy and philosophical. This question has a simple, concrete answer.

The difference between Bayesians and Frequentists is in the loss function that they attempt to minimize.

Bayesian loss functions assume a constant dataset and sums across one's hypothesis set.

Frequentist loss functions assume a constant hypothesis and sum over across possible datasets.

https://en.wikipedia.org/wiki/Loss_function

Really though this is false dichotomy, as it's perfectly possible to be both a Bayesian and a Frequentist by using a loss function which sums over both one's hypothesis set and across possible datasets.