This is essentially the debate between scientific realists and anti-realists in philosophy of science. Realists hold that unobservable entities postulated by scientific theories are still "real"; anti-realists hold that these entities are not real. One of the big problems for anti-realists, as you pointed out with your first example, is that "what is observable" changes over time (e.g. we can now "see" atoms in ways that would have startled physicists in the 1860's). However, the anti-realists do have one interesting argument in their favor: many theories that were empirically successful for a long period of time turned out to postulate unobservable entities that didn't actually exist. For example: ether, which made claims that were useful as prediction tools but didn't truly reflect reality. (This argument comes from Bas Van Fraassen, a leading anti-realist.)

Hopefully this historical context is helpful. The point I am trying to make is this: your question is one of those "great unsolved problems in philosophy."