I also think it’s basically asking “how much do you earn?” Because if they ask not only where you work, job title, it can easily be found out. Or if you work for a Local Authority it can! I think it’s very intrusive
Do you honestly believe they're going to be on Google as soon as your back is turned trying to find out your exact salary? Isn't it more likely that they're just making conversation? Literally any question can feel intrusive to the person being asked if it touches a nerve or if someone is really worried about giving any information about themselves away.
Do you have children? Definitely intrusive, could be uncomfortable or upsetting for many reasons, including infertility or loss.
Whereabouts do you live? Can't ask that, they might think you're going to look up house prices to try to figure out how much money they've got!
Where did you grow up? They might have had a difficult childhood and not want to be reminded of it, also you could be trying to find out if they come from a well off family or not.
What are your hobbies? Maybe they have had to give up their hobbies due to COL, or they might worry their hobbies aren't 'interesting' enough and feel awkward, or they might thinknyou're trying to determine how much money they've got by how expensive the hobby is!
Pets? Their beloved pet might have just been PTS, or maybe their ex got to keep the dog in a painful separation.
Holidays? Maybe they can't afford them and you'll come across insensitive, of they'll think you're trying to find out how much money they've got by what type of holiday they go on.
What do you think about (insert news story/current affairs issue)? Could be controversial, especially with the polarised state of politics atm. You could be trying to determine how they vote or their social class.
What are we left with then, other than "seen any good films lately?"