South mountain in Nova Scotia, Canada. There was (still is?) a family (the Goler clan) famous for poverty, sexual abuse, and inbreeding. A bunch of them were arrested for sexual abuse in the 1980s. Rumor has it, they inspired the Xfiles episode "Home".
Speaking only on the incest stereotype, Spanish Wells in the Bahamas. They’re known for strictly dating and marrying other fellow islanders, which at this point is basically one large family.
Podlasie in Poland, definitely.
My friend's parents have both the same maiden name despite not being closely related. Their whole village has basically the same surname.
In Costa Rica its a subdivision of a province, San Carlos. Very famous for incest (not being taboo). In the costa rican subreddit there was a long thread about it not too long ago. The thread mostly contained anecdotal but has interesting comments; a doctor that sees lots of teenage pregnancy cases, a story of a priest that refused to continue marrying cousins in a small town.
The fact we have an idiom "sent to Coventry" meaning to deliberately ostracise someone should tell you all you need to know.
I went to uni in that city; there isn't enough money in all the world to make me go back there. City of 300k people with over 3k homeless. Utter monstrosity of brutalist architecture (the university library is based on a panopticon prison, I kid you not). And the ring road! Taking your life in your hand just merging into it!
Absolutely insane amount of crime, with one of the highest rates of child sexual abuse in the country (for context, it's crime index is about 20% higher than London's). And I've never seen so many street walkers in my life! Plus they charge, I am not joking, £20 a go.
It's either the Free State or Limpopo. Though if I had to pick one it would be Limpopo, it's the only province where the majority of white people voted to keep and continue apartheid during the referendum in 1992. While I've never been to the US, that sounds like it would fit the Alabama stereotype. Though jokes about dating cousins is usually aimed at people from Brakpan and Danville, but those are specific towns which have their own character.
I don't know. There is multiple possibilities here. Maybe Appenzell Innerrhoden where you're at a low degree cousin of one of the members of the council at the head of the Canton. AI has just 16k inhabitants.
But if you ask a French speaker, it will be Jura. It remember me once I went there. I saw a young woman not older than 25. She was definitely not rich. She already had 3 pregnancies and was outside in a cold foggy morning with the 3 kids walking around the small town. The region has the reputation of alcoholism too.
In Denmark the closest we come to the "marrying cousins" stereotype would be southern Jutland although that trope can be used about all rural areas.
As for being backwards and reactionary, rural Jutland is the place to go.
As for rural poverty and hopelessness an area stretching from northern, western and southern Jutland, over southern Funen to the islands of Lolland and Falster is known as "the rotten banana". Rural poverty is worst on the northern Jutland island of Mors and the island of Lolland.
Võru province in southeastern :estonia-burning: because it overwhelmingly voted for the Fatherland party, which is basically the Conservatives but worse because they are a huge kiss-arse for Isnotreal and want to kill the public healthcare system.
If marrying cousins is the criteria, it's probably somewhere like Leeds in the UK, not because of any British culture of cousin marriage but the high Asian populations there that have a lot of arranged marriage between cousins.