This is about 180 degrees from all of my experience with NYC and New Yorkers. I find New Yorkers to be extremely tribal, and many of them are also extremely efficient at identifying folks from other tribes who may kind of look like them (at least from an outsider point of view).
To be fair, much of this tribalism may not be based on things like race or religious/church affiliation -- as you mentioned, that would make living and working in NYC extremely difficult.
That said, things like career field, social status, and how you spend your free time seem to matter quite a bit.
As a simple example, take your random high SES resident of the Upper East Side and have them go into a grocery store in a low SES neighborhood (race doesn't matter) and strike up a casual conversation with the cashier. It will be extremely awkward, and everyone will be looking at them. Flip the script and have someone from that same low SES neighborhood go to a grocery store in the nicer parts of the Upper East Side and do the same -- this will also most likely be awkward with everyone looking at them.
The example above uses two fairly extreme examples, but this happens along much finer lines as well. Where did people go to undergrad/grad? Where do people shop? Where do they go out? What neigborhood/building do they live in? What do they do in their spare time? All of these things are hyper-efficient shibboleths in NYC that largely do not matter in a random small town in the Midwest -- that is, you probably didn't go to college (one of the two state Us if you did), you shop at the only store in town or the nearest store if there are more than one, etc.
I imagine if you looked into it, New Yorkers would be much more likely to hire a New Yorkers over a New Jerseyan with similar credentials.
Globally, yes, but these suburbs are different because many of these people have lived in the city. NYC has fantastic commuter transportation. People move to manhattan for a job, get married, have a kid, move to the suburbs, and continue to work in manhattan. Their children grow up going to the city on the weekends and move there when they graduate college. The manhattan population is 1.6m, but on any given weekday there are 4m people on the island. 750k people go through grand central every day (Westchester/Fairfield), Penn station another 300k (Long Island). The PATH has another 200k (New Jersey). This is all while excluding the drivers.
> I imagine this has influence on hiring.
I'm not sure how I could convince you, but I've lived here my entire life. There is absolutely no difference between people in the suburbs and in the city because they are the same people.
Like, New Jerseyans think New Yorkers are snobby, New Yorkers think New Jerseyans are sleazy and uncultured, but you'd never, ever expect people to have a problem working or living together because of the difference. Everyone is so mixed-up that "stick to your own kind" becomes nearly impossible. Saying that we live in the same neighborhood and send our kids to the same school, say, but attend a different church, and so we're not really members of a common community, would just not make sense. If you tried that, you'd run out of "people like us" in about five minutes.