The reason for this is not generally applicable outside extremely homogeneous populations.

Where you get ultra-low crime is when you combine that homogeneity with good public education. Take a look at the education systems and levels in places like Japan or Norway, and then compare to Appalachia or Sicily or various middle eastern nations. Also look at the levels of religiosity.

I've come to believe that the potential to rise in social position is what matters most, except possibly in Zoroastrian societies. Appalachia, Sicily (including lower-class parts of Boston), and the Middle East all agree that where you were born is where you'll stay, and that ambition is ridiculous or contemptible; while the healthiest societies are the ones where talent can bubble to the top even if you're not the judge's son.

My favorite example of the vitality that social mobility brings is the Ibo of Nigeria -- "the Jews of Africa", the most successful and energetic of West African peoples. Also look at the dynamic nature of the early Islamic world, compared compared to the stagnant nature of the modern one. And what's true of the Islamic world is equally true of the Iberian one; Brazil and West Virginia have the same basic problem. And back in the Middle Ages, too, it was the most fluid societies -- Lombardy, England, the Low Countries, and the Iberian states -- that were the most successful ones.

Also, I never said that religiosity by itself would result in downfall of a society. Lots of religious societies have done well in history, but they also had relatively good education. The early Islamic world you mention I think qualifies here. It's when you combine religiosity with terrible education that you're really doomed. The education serves as a check against the religiosity getting out of control and turning into theocracy, or whatever you call the wackiness we're seeing in the right-wing here in America today.

I think that the American right is a unique sort of society, and that patterns drawn from their behavior can't be relied on in most other contexts. Their religions look like Christianity but act like non-syncretistic paganism ("worshiping oneself in the guise of worshiping God"), and their hostility to an awful lot of scholarship seems to originate in not wanting to be taken for a ride -- and in the confidence of many peoples, especially relatively backwards ones, that they already know everything that's necessary in order to live well. (The Persians told Chardin as much in the 1500s, as mentioned in The Structures of Everyday Life.)

Have you read Albion's Seed? If not (and it's about 600 pages of historical scholarship, so I won't blame you), look up Slate Star Codex's review, which makes the book's essential points in reduced (and maybe slightly caricatured) form.

Probably, these days, everyone has something better to do.

Edit: perhaps the grandparent comment meant that crime in England was "a lot worse" than in Japan? If so, then yes that's true.

From what I can tell, in European countries the divide isn't so stark and middle-class-and-up people are more likely to be victims of petty and street crime like muggings. Here, if you're a white suburban dweller, you just don't have to worry about being victimized in a mugging or carjacking very much, while in the ghettos you definitely do.