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.