I agree we should care about future people who we think are probably going to exist, for example caring about climate change as it will affect future people who we know will exist.
Where longtermism might go wrong is when one says there is a moral obligation to bring more people into existence. For example under total utilitarianism one might argue that we have an obligation to bring an enormous number of people into existence. I think this is wrong. I've seen longtermists argue that extinction is bad not just because of the harm it might do to present people but because of the 10^n future people who don't get to exist. I see this as wrong. There's no harm done by not having children. This is a very dangerous pro-life type argument. It says there is essentially infinite value in all these potential future people and would justify torturing everyone alive today if it guaranteed the existence of these future people.