To quote Mel Brooks, "It's good to be the king!"=
Practically all Northern Europeans are at least 4th or 5th cousins. That’s because as you go back in time, there are far fewer people. And because kings had a lot of progeny (legitimate and illegitimate) we are likely all of us of royal descent in some sense. Big deal.
You are not far from the truth.
Some say 30%, some say 60% of the European, especially English, immigrants here in the states are descendants of nobility.
My family are descendants of them. Earliest we’ve found is Edward the 3rd as far as royalty is concerned.
Discussing this at our family gathering i told them to think on this...”Leave early, stay long, return late.”
Understand that and you’ll understand a lot of why a lot are descendants.
That is a gross exaggeration and distortion!
To be merely 4th cousins, they would all have to have a set of great-great-great-grandparents in common. Even in a single, small country like Iceland, that would not be the case. (A significant fraction of the total population of Iceland being 6th cousins, I could believe - and the country maintains a freely-accessible database so that romantic partners can check for any significant consanguinity.)
But to speak of "all Northern Europeans" being 4th or at least 5th cousins is absurd. For that statement to be true, a randomly selected person from, say, Dublin would have to always have one set of great-great-great-great-great-grandparents in common with another person from, say, Helsinki.
You might like to consider revising your claim to, for instance:
In any given medium-sized town in Northern Europe, there is an appreciable chance (~ 20%) that a randomly-selected inhabitant is fifth cousins (or closer) with another randomly-selected inhabitant from that same medium-sized town.And even that guarded statement might be true only for the beginning of the 20th century or earlier.
Regards,