I'm upset by many things going on in the world but I'm not overwhelmed because there are no relevant decisions for me to make. Look at it this way: what's the difference between reading a book that says Genghis Khan killed a hundred more people than you thought he did centuries ago and reading a newspaper that says a hundred people died in some catastrophe yesterday? In both cases, you've learned that total strangers died in the past, there was nothing you could have done, and there will be no direct effect on your own life. It's natural to be more upset by the more recent deaths (and I admit that I would be) but I think it isn't logical.
The exception to that is AI. I think I do need to change my own life in order to increase my chance of thriving in an AI-dominated future, at least because if some jobs will still exist then I'll need to be able to do one of them.
(I suppose "Do I flee the country?" is another decision I technically need to consider, but the answer is "No unless things get dramatically worse." Thus there isn't much to think about on a daily basis.)
I think people's behavior is determined much more by social conventions and the expectations of their community (in addition to pragmatic self-interest) than it is by logical reasoning. I'll risk being the preachy vegetarian by discussing people's attitudes towards eating meat. Most people sincerely believe that cruelty to animals is wrong, and also that factory farming (if not all killing) is cruel. Yet they eat meat. I even know some people who started eating meat again after being ethical vegetarians. Did they change their minds about whether or not harming animals is bad? No. If pressed, they feel guilty but they don't like to talk about it. The reason they're eating meat is because it's convenient and almost everyone expects them to, not because they reasoned from first principles. Likewise with religion - if no one else is giving everything away to the poor and everyone will think you're crazy if you do rather than praising you, you're not going to give everything away to the poor even if it would make sense to do so given what you believe.
Edit: Kidney donation is another example. I met a woman once who donated a kidney to a friend of her mother's. This person wasn't someone particularly dear to her, but she found out that he needed a kidney to live and she gave him hers. I think that what she did is commendable, but I still have both my kidneys. This is despite the fact that I sincerely believe that if, for example, I saw a drowning child then I would risk my life to save him. People would think I was a hero if I saved the child, or that I was a coward if I didn't try. Meanwhile almost everyone I know would think I went crazy if I donated a kidney to a stranger. My relatives would be extremely worried, and they would try to talk me out of it. I'm not going to do something difficult, painful, and (to an extent) dangerous when everyone I know would disapprove, even if in principle I think risking my life to save another's is a good thing to do.