English equivalent of Polish saying "A yokel can leave a village, but village will never leave yokel"
Solution 1:
The Polish phrase itself is actually fairly well known, albeit slight re-worded. I've heard it for various regions: "You can take a man out of the [south|north|country|city], but you can't take the [south|north|country|city] out of the man."
I think I've even seen it on a T-shirt.
Solution 2:
According to Oxford Dictionaries, “Once a _______, always a _______” is another way to say that
A person cannot change their fundamental nature: once a whiner, always a whiner
In your contexts the blanks could be filled with whatever captures the nature of village, non-city-dwelling that you’re after: country bumpkin or country gentleman, for example, or maybe the word used for people from a particular village (Podunker, for example) or even just the word "villager."
Solution 3:
A slightly more generic term would be 'a leopard cannot change its spots' which means that the way you're born is unalterable.