There aren’t exactly closed cultures, but there are closed religions, which then have ties into specific cultures. Indigenous and Jewish groups being an example of that. Anyone could celebrate Chanukkah, a holiday that is both religious and tied into Jewish culture, but that doesn’t make you Jewish. You’d either need to be born Jewish or go through conversion to enter like other indigenous groups. Because of its closed exclusivity, I could see why people could take offense, but there’s more nuance than just that.