Why care about anyone? Why not just take out as much on as many as you can as quick as you can?
The answer to the question - or part of it - is that we are called by Christ to love one another. That idea’s not confined to Christians, but it’s part of Christianity: as is belief in a Hell - & the motive for such love is distinctively Christian. If we accept there is a Hell, it seems illogical to reject the requirement of Christ that we should love one another. Why should we think of Hell at all, if we don’t think of the very sort of behaviour that makes going to Hell impossible ? The two things, the threat of Hell & love of one another, come to us from the same Christ. Besides: the times we are tempted to despair are when hope is most necessary
Fatalism & determinism are totally anti-Christian - so one cannot know for sure one is going to Hell anyway. But why believe there is a Hell, on the testimony of Christ, while adopting an anti-Christian notion such as fatalism ? Christ is the Saviour from fatalism & determinism - that is one of the reasons Christianity appealed to people in the Mediterranean world. He rules; chance, destiny, or the stars don’t: He does so for He “has ascended above the heavens”; & as St. Paul says.
Even if we were not Christians, it would still be unnatural to harm others; even reason alone can make this clear: for we & they have the same nature, so that just as we are human, so are they, & should be treated humanely; just as we would hope for from them. It’s illogical, as well as nihilistic & selfish, for us to harm others because we despair of salvation; despair & doing wrong to others, will make our damnation certain; so to harm them is silly.

It is no fault of others that we are (we suppose) going to Hell - which is why it is so illogical to wrong them.
The idea that only
I matter, & that everything in creation centres on
me,
me,
me, is a debased bit of modern egotism. The pagan philosophers knew better than that: Socrates had no Paradise to hope for, & neither did Epicurus or a host of others: but their lack of hope did not become a reason, or an excuse, for maltreating others. So how can we behave worse than they did ?
So there are lots of reasons to care for others. Hope that helps.