Harry and Meghan are first cousins? Wow, every day's a school day round here. 🤣 Harry does have quite a few cousins actually (I think 18 first cousins but don't quote me), but none of them appear to be related to the Markles. Unless Harry had a secret affair no one knows about...
On a very sad note, his and William's first cousin once removed, Rosie Roche, was literally just found dead at only 20 from an apparent self-inflicted gunshot wound. 🙏
As for Obama, yes, he is actually distantly related to Dick Cheney if you go 8 or 9 generations back, and also apparently shares a family tree with George Dubya, Harry S Truman, and Lyndon B Johnson, among others.
As for the King John thing, I'm not a geneticist, but apparently it's not as far-fetched as it sounds. Everyone in the US with some European ancestry may well share some link to a bunch of famous people including monarchs.
Go back far enough, and we all have millions of ancestors because each generation doubles as you go back in the family tree so the number of ancestors goes up exponentially. 2, 4, 8, 16, 32, 64, etc.
(It would actually be far more: go back 30 generations and you'd technically have over 2 billion theoretical ancestors, more than the global population at that time. But due to a common phenomenon known as pedigree collapse, which means when people marry and have kids with people they're actually related to (even distantly), the real number is far lower.)
But after a dozen or so generations, the DNA is so "diluted" as to be effectively meaningless.
So not so much coincidence or conspiracy as just the marvels of math and genealogy.
TL;DR: We're all one big happy dysfunctional family lol. No wonder we fight so much.