(Never Mind the INTRO) He did not ask you if they were true or not. He asked if it was, “Okay to Stereotype.” (I see you did respond to that initially.) You hit the nail on the head calling them silly. You could even assert, that we all do it. Our brains are just wired to lump shit together. Hey! They work just like our asses in that regard.
Is it Okay? When you know you do it and when you can think critically around your own bullshit… it has to be okay. Imagine functioning in a world where there was no stereotyping. How could one tell the cowboys from the Indians, the biker gangs from the kids on trikes, the housewives from the heroine-addicted hookers? (Anyone who sees distinct categories in anything I have mentioned has not yet read deep enough or learned to critically think about their ability to stereotype.)
So, is it okay? I think it is necessary. We don’t have time to sit and figure out every interaction we have with other human beings. So, ‘Yes,’ there are times when it is okay. There are also times when it can make you look like a dumbass. “So, Be Careful.”