Sure, no event from the objects past the Hubble radius will be able to affect you if the universe does not change drastically. If it was to start shrinking in the future, then what happened outside our horizon today could end up influencing our physics tomorrow.
It is correct to say that what happens outside the Hubble horizon is non falsifiable. Therefore it matters cum grano salis: you may use our physics laws to get an idea of what is happening beyond the Hubble radius (like "yeah, I am very positive saying that the star will go supernova N days after we see it crossing the horizon"), but you can never disprove anything, which makes those predictions completely useless for scientific purposes. That does not mean that it makes zero sense to say that the star will go supernova after N days, it means that you cannot use this statement to make any rational leverage on any scientific argument.
Conservation laws are a little advantaged in this matter: you can define a conservation law on a ball of a certain radius (like: the momentum change inside this ball is equal to the incoming forces through its boundary). By chaining a lot of balls (smaller than Hubble radius) together you can patch regions which are bigger than the Hubble radius and therefore formulating the initial conservation law on scales bigger than Hubble radius.
Even though the mathematics seems solid, this conservation law reasoning is non disprovable too: you see that a lot of matter is vanishing through the Hubble horizon; how can you be sure there is the same amount of matter on the other side after it went through? If one replies: "I suppose the conservation of matter works on smaller scales than Hubble radius and I patch a lot of conservation balls together", how can you go the ends of the observable universe and prove if he is wrong?
Even so, these conclusions are the ones we tend to take for granted because of the so called Hoccam Razor: instead of finding a new explanation as for why the conservation laws cease to be valid we just assume they are, since we have no reason to believe we are special observers. But could it be possible to falsify the statement that we are not special?
I am no expert in philosophy so correct me if I was mistaken, I just felt like giving it a shot. Unfortunately I am not aware of any literature besides obviously Popper's classic "Conjectures and Refutations", which you seem to be familiar with.