I feel guilty for not living in ways that would be approved of by our ancestors.

Presumably by staying on the lookout for opportunities to get their hands on a time machine.

Hand me a time machine and you'll find out!

If I'm correctly understanding the subtext of that question ("if it doesn't affect what you actually do besides talking, it's meaningless to say you care about it") then I respectfully disagree.

I am quite happy to say that A cares about B if, e.g., A's happiness is greatly affected by B. If it happens that A is able to have substantial effect on B, then (1) we may actually be more interested in the question "what if anything does A do about B?", which could also be expressed as "does A care about B?", and (2) if the answer is that A doesn't do anything about B, then we might well doubt A's claims that her happiness is greatly affected by B. But in cases like this one -- where, so far as we know, there is and could be nothing whatever that A can do to affect B -- I suggest that "cares about" should be taken to mean something like "has her happiness affected by", and that asking what A does about B is simply a wrong response.

(Note 1. I am aware that I may be quite wrong about the subtext of the question. If an answer along the lines of "It manifests itself as changes in my emotional state when I discover new things about the lives of people 5000 years ago or when I imagine different ways their lives might have been" would have satisfied you, then the above is aimed not at you but at a hypothetical version of you who meant something else by the question.)

(Note 2. You might say that caring about something you can't influence is pointless and irrelevant. That might be correct, though I'm not entirely convinced, but in any case "how does that caring manifest itself?" seems like a strange thing to say to make that point.)