No. They believe you can measure an infinite number of trials (say # of heads vs tails) and whatever ratio you get is the probability of heads.

However it's problematic because you can measure a million coin flips and get heads every time. It's not possible to actually measure an infinite number of trials - you need to imagine it.

This is just silly, nobody in their right mind would believe they could do something “an infinite number” of times.

If you don’t do an infinite number of trials then you can’t be sure your frequencies match the real probability.

They still non-trivially define/demarcate what the population actually is. That is kind of a belief because it is a choice not given by nature, and there are infinitely many choices one could choose.

Nature does not give you choice, it gives you the frequency (say, in the form of the intensity of a spectral line of an atom), and it is the base of the scientific method to listen to what nature is trying to tell you. There is nothing subjective in this process. Arguing otherwise is like saying that atheists “believe” in the non-existence of god.

Nature is telling you an infinite number of things, the process of selecting what to measure and what to exclude in the measurement is a choice.

In terms of frequentism, how you define what the population distribution you are sampling from is exactly, is a choice.

You are limiting the discussion to what happens after you've chosen how and what the population distribution consists of.. that part is itself a nontrivial and subjective process.