Identity politics is the belief that your political ideology should be determined by your identity, e.g. that you would/should have distinctly different political aims if you're a woman compared to if you were a man; black or not-white compared to white; religious compared to secular; ...
While such studies and the resulting politics became very popular on universities in the noughties and while Jordan Peterson is currently talking them up on the internet, that's not what has eliminated bipartisanship and the loss in the middle when it comes to D and R. (There are increasingly fewer registered D and R compared to Independent voters too.)
The split that lost the middle was caused by political partisanship and attack politics (negative campaigning) and at this point (decade) it has turned congress into a shitshow of governing (why the low approval rates).
What caused the loss of the center and the gridlock:
- The Hastert rule: Not allowing a vote on the floor of the house unless a majority of the majority (THE RULING PARTY) allows it. It doesn't take much social/strategic intelligence to see how this would create a gap in the middle. If you're a moderate, you first have to convince the extreme-wings on your own side before you can even begin to work with moderates on the other side.
- Talk radio, C-Span, Fox News and Newt Gingrich: It used to be that Americans read and watched the same things and thus shared the same facts and frameworks. This makes for a nice bell curve in terms of the center. In the 90s a bunch of media was created on the right creating a very conservative spin. Gingrich would hold speeches for empty rooms in congress but you could not see the empty room on C-SPAN. These clips would then be used on Fox et al. As a result, the facts/frameworks became bimodal resulting in the old center and the new right. (This also shifts the middle.---The middle is not between NPR and Sean Hannity ... it's between Hannity and Maddow on MSNBC, but taking the average of extreme outliers is not going to reveal what/where the center framework is) Only within the past decade has there been similar outlets with very liberal spins. For each left-wing talk radio host you can find (if you can even find one), I'll find two^H^H^Hfive on the right. Basically, in terms of media spin, the left is 20 years behind the right, but they're catching up, mostly on the internet. Meanwhile, people who watch Fox or read Drudge or Breitbart are correspondingly so far off the center that they think the actual center is the left.
- Loss of Senate traditions: If the Hastert rule turned the House into Us vs Them, the Democrats' frivolous use of filibusters (from the noughties and into the present) against Bush2's court nominees despite the nominee having [simple majority] support in the Senate making what is supposed to an exceptional political weapon, a standard tool of politics. This was escalated by D's using the nuclear option once they gained Senate control to thwart R's using the filibuster in the same way. The last remaining exception (supreme court justices) to these shenanigans was then (justifiably---hard to argue otherwise) nuked by R (Mitch McConnell) as Gorsuch was installed with a simple majority. The Senate has thus gone from a supposedly voice of moderation with a 60-vote rule for serious stuff and a long term view (see Ben Sasse for someone who still admits that much) to a simple majority tyranny.
- Citizens United and superpacs and shameless [software optimized] gerrymandering: Thus ensuring that not only are politicians (mostly on the red side) not representing a majority of voters; the politicians are also actively voting against the majority interests (but for the superpac interests). For example, a majority (larger than the D/R ratio) of voters did not want the tax cuts and do want to keep ACA. The fact that democracy is deliberatively made unrepresentative so politicians can stay in power also draws up the lines and tightens partisanship. If D holds the majorities in 2020 and gets to redraw the gerrymandered districts in their favor, I doubt they're going to be fair about it wanting revenge for 2010.
So, I'm not buying that this crack down the middle happened due to political correctness or identity politics. That's just a framework that's currently popular/fashionable on the internet thanks to Jordan Peterson and a few others. It happened by path-dependent construction of the structure of the political process and the way politics has been communicated to the voters since the 1990s.
If current politics is decided by any kind of identity, it's whether you wear a red shirt (and watch one kind of news) or whether you wear a blue shirt (and watch another kind of news). The level of information/thought that goes into picking a shirt is materially higher on this forum than for the average voter. Most people do not pick their party. Their party picks them and then give them the memes ("Tariffs are Great") and soundbytes ("But her emails", "Nevertheless, she persisted") to justify their shirt color for them. Most people are idiots^H^H^H^H^Hhelpless.
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Going back to the OP issue.
I figure this is just the latest salvo in the "war on immigrants" coming out of the mind of Stephen Miller who is also responsible for such great hits as the Travel/Muslim-Ban, the failure to resolve DACA, the family separation policy at the border, and now this. He's essentially the nativist wing of the white house---also one of the remaining few who has been with this administration since the beginning.
I think nativism could be classified as a kind of identity politics but if so, it applies to the largest possible group in the country, namely Americans, which is something like 85% of the population. As an identity politic, this makes it much larger than even feminism at <51% (insofar all women were automatically considered feminists). Normally and crucially identity politics is pursued by a minority who feel they're being oppressed by a majority. That's certainly not the case here. Rather, this is the case of the majority going after a minority. Therefore, calling it identity politics is a bit of a stretch.
However, given the political situation and the general lack of information/framework in the average voter, it's certainly possible to present it as a kind of identity politics in terms of slogans, etc. "Build the wall" and scare-mongering ("Bad rapists from MS-13"). You can even convince people that immigrants are taking their jobs even though no natives seem to want to pick apples at $6/hr. However, such understanding is much more complex than the simple "Immigrants are taking our jobs" or "Build the wall" which fit on a stupid facebook meme.
Naturally, being an immigrant, I'm VERY VERY interested in this(*). So far I've seen three or four individual news reports with headlines that are something like this: "Trump supporter's wife/husband gets deported". Then there's an interview, an inevitably, the Trump-voter will say something like "I never thought this would happen to me" and "I thought Trump was only talking about deporting those bad people". It hasn't quite sunk in that ICE is going after everybody they possibly can in order to meet the quotas, including stuff that most Americans would not see as qualifying as being a "bad person" if they had done it themselves---which they likely have (80 million Americans have an arrest record, 47% have received some kind of public benefit at some point).
(*) I'm still safe, but damn was this one close. About four days ago, I was talking to DW about the recent hike in corporate health insurance and suggesting maybe we should look into the exchanges this year. And as noted by iDave above, until this year, it was practically mandatory if not strongly encouraged anyway to get insurance via ACA anyway.
There's a lot of humans who are absolutely okay with reducing benefits (recall how well that "welfare queen" concept is still playing) or hurting people as long as they don't need the benefits themselves or the pain is inflicted on other people. There's basically no sympathy outside "me and my family" on the emotional scale and no empathy on the cognitive scale. Then when they lose their job and need the benefits themselves, they fell they deserve them---and when the immigration policy they voted for causes their spouse to be deported for accepting unemployment benefits or getting a speeding ticket, they're weirdly surprised. I've had this discussion with people I know personally and for whatever reason they do not experience any cognitive dissonance between their actions and the consequences of their political beliefs until it hits them like a brick in their face. (Best explained by how 70% are Kegan2 or Kegan3 and thus literally do not grok the consequences and values of laws beyond how they affect them personally in the here and now.) Basically, they have to learn things the hard way.
It's estimated that this could affect around 20 million people(+). I frankly hope all the families whose toes will be stepped on will be Trump-voters. That would be karma. I can't find find any sympathy within myself for these cases anymore.
(+) Natives are more likely to receive some kind of benefit than immigrants (Imagine that

... well, it's not suprising. Many immigrants are excluded anyway or wouldn't know about the benefits in the first place.) and lots and lots of people receive or have received something from the government. (Strangely, the child tax credit was not on Miller's list, huh?)