I don’t know your friend and don’t know what she understands by cultured. She probably means either:
A) A ghastly, pretentious, fake family. The sort of people who have made some money and try to justify their big house by taking an interest in ‘culture’. After all, they’re superior to the herd now, so they’d better start proving it. Unfortunately, they don’t have the brains or the taste to back it up. The parents speak with a forced ‘upper class’ accent. They send their kids to private schools. They go to art exhibitions and museums that bore them to death. They listen to classical music, which they’ve convinced themselves they really enjoy (they don’t). They’re learning Italian, because they’ve realised that Tuscany is where the cultured people go (only oiks go to Spain), but aren’t really getting anywhere. Everything seems strained and fake.
B) A family of true art and literature lovers. Friendly, smiley and polite, but totally unpretentious. Maybe the parents are university lecturers. Or maybe they met while doing a post-graduate degree in philosophy or literature. There is probably brains in the family - a grandfather who lectured at Oxford, or something like that. The house is scruffy and chaotic, with piles of books everywhere, a piano covered in beer cans and empty coffee mugs, the walls covered in wonky paintings and movie posters. There are scruffy dogs, kids running and shouting, and constant laughter. They swig beer out of cans, smoke weed now and then, have piles of records everywhere, and are generally kind and loving and friendly.
My (gay) neighbour is a very cultured person. He’s got an MA in literature and lives in a flat surrounded by books. But like all truly cultured people he’s completely unpretentious. The first sign of a pseud is that the books are all clean and neatly lined up. In his case, the books are everywhere - piled up in the kitchen, the bathroom, stacked in corners, etc. And they are battered. There is also a crazy assortment. If you run your eyes over his book shelves, you see Great Expectations and King Lear and Bertrand Russell next to Bart Simpson’s Guide to Life. Then you get Nabokov and William Blake and Carlo Rovelli followed by Asterix comics and The Book of Crap Towns. He goes to art exhibitions or museums all the time, but he doesn’t tell anyone. He does it because it gives him pleasure, not to impress.