Someone told me not to ask strangers how their day was (like in the real world) if I didn’t really want to know (like that someone’s dad died)

To be fair, this is cultural. I’m an American immigrant in Germany, and I’ve unintentionally started that type of conversation a bunch of times. Here, if you ask, it’s not a social cliche, so you shouldn’t be unprepared for a real answer. In American terms, it’d be like putting your hand on someone’s shoulder, looking them in the eye for a moment and asking “how are you?,” then being surprised if they tell you something sad.

Someone told me not to ask strangers how their day was (like in the real world) if I didn’t really want to know

Learn how "how are you doing" is different from "how are you feeling".