You're right it reduces to Bayesian vs frequentist views of probability. But you seem to be taking an adamantly frequentist view yourself.
Imagine you're not interested in whether a dice is weighted (in fact assume that it is fair in every reasonable sense), but instead you want to know the outcome of a specific roll. What if that roll has already happened, but you haven't seen it? I've cheekily covered up the dice with my hand straight after I rolled it. It's no longer random at all, in at least some philosophical points of view, because its outcome is now 100% determined. If you're only concerned about "the property of the dice itself" are you now only concerned with the property of the roll itself? It's done and dusted. So the entropy of that "random variable" (which only has one outcome, of probability 1) is 0.
This is actually a valid philosophical point of view. But people that act as though the outcome is still random, allow themselves to use probability theory as if it hadn't been rolled yet, are going to win a lot more games of chance than those that refuse to.
Maybe this all seems like a straw man. Have I argued against anything you actually said in your post? Yes I have: your core disagreement with OP's statement "entropy is a property of an individual". You see, when I covered up the dice with my hand, I did see it. So if you take the Bayesian view of probability and allow yourself to consider that dice roll probabilistically, then you and I really do have different views about the probability distribution of that dice roll and therefore the entropy. If I tell a third person, secretly and honestly, that the dice roll is even then they have yet another view of the entropy of the same dice roll! All at the same time and all perfectly valid.