They are real but greatly exaggerated by people using the aforementioned rhetoric and completely surmountable. People who claim they aren't are either trying to push an agenda (usually on authoritarian, nationalistic, and/or warmongering grounds), or not very well-traveled or have very narrow social circles not involving foreigners at all.

Your 12th century stories are interesting and all but do not reflect the reality of the world we currently live in. If you live in a large city and have a medium-to-high salary, which is a reasonable assumption to make given HN's demographics, it is in fact easy to get acquainted to other cultures by traveling often (possibly living abroad), learning other languages and/or befriending (or dating) foreigners. Much easier than used to be a couple centuries ago, in any case. If you do, you will find that deep down beneath the veneer of culture humans are very much the same. I don't have data to back this up, this is only from my mere experience.

Pretending that cultural differences don't exist is harmful and condescending; acting as though they were insurmountable and irreconcilable is downright dangerous and leads to disaster.