At my job there are a buttload of people who are always late. This is upsetting to me because I always have to pick up their slack. So I complained to the manager but I was told other people being late all the time “isn’t my business”. When I have to do the work of two people, or end up late to other obligations because I had to stay till my replacement arrived, other people being late is my business. What do y’all think about this situation?

Unless your boss is personal friends with these people, I don't see the issue. If it's an actual issue, and they're not friends, no boss is going to let that go on long without at LEAST a write up.

Also, about leaving on time, your work can't keep you there. If you HAVE to leave, and that leaves them short, tough shit. That's on the boss to pick up the slack.

How late are they, and is it a lot of extra work as a result of it?

I agree with Chippy you shouldn't be forced to stay late in either scenario

The guy who runs the coffee shop comes in an hour late every day and customers come over and complain to me about not getting their coffee. Then the one guy who runs self checkout (what I do) is 15-20 minutes late almost every time. And when cashiers call out/come in late, I get forced to run a regular checkout and run back and forth between the departments.

He's an HOUR late every day, and still has his job? Is it his own shop and he gets to choose when to start, or is he just an employee? 20 min late for a cashier seems egregious as well

Just an employee. I think it’s ridiculous he says he commutes from far away but that’s no excuse IMO.

You should get a new job. You are not getting rewarded for being a good employee and are being dragged down. This place is not going to survive long term anyway being run like that. It's a sinking ship - don't go down with it.

But Ryu, WHERE is he going to find another coffee shop?!

Just show up 20 minutes and fuck around on your phone all day. Doesn’t seem like anyone else takes this job too seriously so why stress yourself over it?