I don't see how their argument makes sense, it somehow implies that "our" generation won't see any ill effects yet. That is just trivially wrong if you talk about the environment in general, because whether you think that climate change will be noticeably during "our" lifetime or not, there are things we could do to the environment to make life bad for everyone within a few years. So there needs to be at least some limit to what "we" can do to the environment, assuming we follow that premise in the first place.

Going back to climate change specifically, we can accelerate or decelerate that as well. Are the people you have heard arguing saying that legislation should keep climate change in check, but only in so far as it only affects generations after the current, however that may be defined? Even going with that ridiculous premise, I am not sure how that could be implemented.