What does that responsibility mean? Let's say I accept my responsibility for benefitting from killing all this wildlife and murdering the inhabitants. Now what? Does this change something? Is there some action I should take?
I don't know what the answer is to the question of what actions I (and "we") should take because of my responsibility (and our shared responsibility). I do know that the responsibility I feel is greater the more tightly I am tied to a society or community. I don't feel much responsibility at all for homo sapiens' eradication of Neanderthals (assuming that's what happened). The actions happened too long ago and the "society" is too loose (homo sapiens). I do feel some responsibility for what my country's recent forebears have done; I feel a tie as an American and 100 or 200 years in the past is just a handful of generations.
For me it seems the minimum is to identify myself as an "environmentalist". Many (most?) of the objections to proper care of the environment come from people who argue against it because doing so will lessen business profits by a little bit. Even assuming it's true that it will lessen profits, seems like we need to devote more of our resources to preserving the environment. At a minimum, that should mean that businesses in our society should have to accept somewhat lesser profits (perhaps by being taxed) in exchange for better preservation of the environment.
Also, I have no problem with businesses that affect the environment negatively bearing much more of the cost to replace past harms. In the past, and even now, we've allowed businesses to pollute our environment (air, water, land) without them paying for the damage they've caused. They are among the prime offenders, although everyone does share some responsibility for being part of a society that's let those businesses operate as they have.
Not quite. What I was getting at is this argument is usually presented in the context of blaming the West generally or the United States specifically for various atrocities, and gently eliding how the societies which were aggressed upon were usually no different from a morality standpoint: it was simply a matter of who got to who first with a bigger stick in their hand. Not "everybody does it, so it must be okay," just "everybody does it, so casting blame on a specific group is, paradoxically, unfair."
For that reason, our responsibility to properly safeguard the environment and to ensure the rights of all people cannot be dependent on one nation or culture atoning for some crime their ancestors allegedly committed in the past. That just builds a never-ending tower of recrimination and anger. It has to be simply our obligation as human beings to each other, right now, today.
Also, given that you seem to already agree we have the obligation, your insistence on dis-acknowledging our cultural past as a source of the obligation seems odd. Nobody said the obligation had only a single source. The only reason to get angry, so far as I can see, is if a person thinks current steps are perhaps nice to do, but not obligatory. I fail to see how a "never-ending tower of recrimination and anger" can arise from someone simply giving an additional reason that supports the decision we've already made (that we have an obligation).
Well, look at it this way. If someone had killed my father, I wouldn't be satisfied with them saying "here, I'll pay for your college education and we'll call it even"; I'd want them in the electric chair. Similarly, a focus on alleged crimes of past cultures leads inevitably to angry demands for retribution for said crimes, followed by a lot of people replying -- with absolute justification! -- that they weren't responsible for these past crimes, or maybe the other guys were just as bad. Next thing you know everyone's screaming at each other and the formerly universal values have been turned into a political football. If you've got a concept that should be apolitical and universal, the last thing you want to do is prominently attach it to one side of a bitter cultural war.
Nobody's suggesting you should be tried for the crimes of your ancestors, or previous members of your society. What we can do is stop doing more damage and try to rectify some of it, where it is reasonable and affordable to do so.
There's no law at work here though. If there is some specific issue you are particularly concerned about that happens not to have any such historical link to you, but it bothers you so much that you take a special personal interest in it then that's fine. But even without dedicating our personal resources towards righting the worlds wrongs, as tax payers, consumers and voters we often make decisions that bear on these issues. I think it's worth bearing that in mind.