You could point out that plenty of people also have preferences about the lives of e.g. poor people in developing countries who they could, if they wanted to, just ignore completely. (Or preferences about the lives of strangers in their own country, for that matter.)

This post is relevant. Not sure if your audience has the background to understand it though.

Why "should" I like the taste of ice cream?

I do. I don't have to eat it, and I could trade off the fulfillment of that like for other likes. But I do like it, and that enjoyment is a value to me, I won't give it up except for a greater value, and even if I give it up for a greater value, it wouldn't mean that I had stopped liking the taste of ice cream.

You don't need a reason to value; values are the reasons.

"Yeah, so? You'll be dead, so how/why should you care?"

Or more famously, au reste, après nous, le Déluge.

Perhaps there is difference in understanding the subject matter. People intuitively have preferences about things related personally to them: about their friends and relatives (and enemies), about the impact of their work, about their city or nation. But when you say 'some sort of sapience to keep on living', it is naturally interpreted as relating to very distant future (1) when nothing of that which they care about exists any more. You may, of course, have preferences relating to such a distant future when humanity is replaced by 'some sort of sapience', but many people don't have (2).

In short, I suspect that "you'll be dead" isn't the true reason of their disagreement. It's rather "nothing you care about now will exist".

Footnotes:

(1) Distant doesn't necessarily mean many centuries after present. It's the amount of change to the world which matters.

(2) Me neither. I can't "understand" (for lack of a better word) your preferences on the gut level, but I understand that there is no phase transition between your and my preferences, they are in the same class, yours being more general.

Huh. I just wrote a little blurb about this yesterday. Many individual's utility functions include terms for things that exist outside of themselves. It's trivially simple for one's utility function to be fulfilled by ensuring those things continue even after the person ends.

I am reluctantly someone who pretty much doesn't care about what happens after I die. This is a position I that I don't necessarily endorse, and if I could easily self-modify into the sort of person who did care I would.

I don't think this makes me a monster. I basically behave the same way as people who claim they do care about what happens after they die. That is, I have plans for what happens to my assets if I die. I have life insurance ("free" through work) that pays to my wife if I die. I wouldn't take a billion dollars on the condition that a third world country would blow up the day after I died.

As you say, though, it's "me-of-the-present" that cares about these things. With the self-modification bit above, really what I mean is "I'd like to self-modify into the sort of person who could say that I cared about what happens after I die and not feel compelled to clarify that I really mean that I think good things are good and that acting as if I cared about good things continuing to happen after I die is probably a better strategy to keep good things happening while I'm alive."

Well, the answer is simple to me : the well-being and happiness of other persons, especially my relatives and my friends, but also other humans in general are part of my terminal values. So I care about what will happen to them after I die, as long as they'll be alive. But I don't care much about what would happen after all humanity is wiped out, if that were to happen.

The original debate appeared to be limited to "Live forever" or "Dead forever" and if this was intentional, and we are intentionally ignoring the possibility of death not being permanent because that would be fighting the hypothetical, then the point below is irrelevant.

However, if we should consider the possibility that after a death a person might have a chance of being resurrected by a future sapient, then at that point, keeping future sapients alive might have potential value to that person, even if they didn't care about things that happened when they were dead.

Edit: The second paragraph was originally written in the first person, but it sounded off when I reread it, so I changed the grammar and added slightly more detail.

You could simulate a debate with someone here taking the opposite point of view. Or better yet, you could take the opposite point of view and here someone else carry the argument.