In reality you can, indeed, care about multiple issues at the same time

You say that, but I am learning first hand that I have a finite capacity for injustice and misery. I see awful shit in the news, sometimes far away, but sometimes very close to home and I see it every day. It takes a toll on your mental health, caring about everything, taking a moment to ask yourself "is there something I can do about this?" - it's especially hard when the answer you come up with is "not really".

I think one really does have a limited amount of bandwidth for this kind of thing, and we absolutely have a limited amount of time. So even if you did care about everything, it's certainly not feasible to act on everything. And just carrying all those concerns that you know you're never going to act on, that cannot be healthy.

Sometimes you just need to let something go, say "this is not my concern". I don't believe there's anything wrong with that, so long as you make an effort to decide which things are important enough to care about, even when you're at your limit.