As for your opinion , insisting on assigning a different mindset to rural or "less diverse" parts of the country (as you put it), tread carefully. It makes me wonder, exactly which America you're living in? .
Let me put it to you in numeric terms. A dozen years ago my friend Mahesh moved from Central Indiana to Fremont, California, and enrolled his 7 year old to Fremont Elementary. He calls back and reports "Man, this is an interesting place. Out of 30 kids, 10 are Indian, 10 are Far East / Orient, 7 or 8 are Hispanic, and 2 or 3 are locals". I got a very good chuckle out of it, as he came to Central Indiana in the days where you'd see an Indian guy in the mall and strike a conversation just 'cause there were only a handful of Indians in the whole area code...
Today, in the wealthier suburbs, easily 10-15% of the kids are hyphenated, and being of Indian, Korean, or what not origin is not a big deal. My older child did get some comments from a teacher regarding her 'last name' (ethnic to the last character

) and after reading him and the principal the riot act these comments thankfully stopped.
I don't know how much you've lived in 'Flyover Country' but I've lived for 30 years in places like Michigan and Indiana, and trust you me, it ain't the same as the coasts. It was Leave it to Beaver back then, and it's slowly changing now. If you're talking metropolitan areas, sure, things are now where they were in the more illuminated areas 30 years ago, but if we're talking rural / near rural Midwest, South, etc, Leave It To Beaver, Lassie, white picket fence, etc are all documentaries of current life. Best yet, you won't know by driving thru or watching on TV.
You spoke of accents - now, granted, I have a heavier one (by choice), and speak incredibly fast, as is the norm of my native language, even in English. So we're having an animated conversation with my children at the supermarket checkout and the cashier asks meekly "excuse me, sir, what language are you speaking?". I did not have the heart to tell her it was English (we speak English at home).
Or, proceed to scene two; an after-church party in rural Georgia involving my supervisor (native USC, from Seattle / SoCal) being introduced to a distinguished looking Southern gentleman. So, the gentleman says his name as "Aye-yed" and my boss asks him how to spell it. The gentleman turns red and slooooooowly says "Eeee Deee".
What makes America a great place is that it really is not a monolithic place, but rather, a great mosaic. A Greek guy can choose to live in Astoria, NY and never speak English again; likewise, a Chinese person in Boston's Chinatown (awesome food, make sure you go with a Chinese speaker to order properly); A Frenchman can live in South Louisiana, and so on... But, between all these greatly diverse places there exists.... you guessed it... Flyover Country, and things are not quite the same.
A good way to tell if you're in Flyover Country or not is the size of the local USCIS office. After used to the massive offices in New Orleans and Detroit (New Orleans especially, baguettes and french coffee, then get in line, ah, the great days

) getting to Indianapolis was not quite the same (they since upgraded to much larger facilities, as the foreign born population of the city skyrocketed)
It's a slow process here, as are lots of other things; we still need the monthly trips to Chicago or (of all places) Cincinnati, OH for ethnic groceries (Jungle Jim's has no equal even in SoCal or San Fransisco)... I still have to get used to the idea my younger one is the only non-blond kid in the Jr. High Choir

, you get the idea.
In essense, this change, adaptation from all sides, is what makes it so great a place.
Gotta run, I am cooking some strange Middle Eastern fried dumplings for dessert!