That seems to depend on situation and audience for once, and level of anticipated misunderstandings, as there is obviously no firmly established and well defined single word for it/'them'. But a few connected concepts and close contenders seem imaginable. Especially fitting seems Judith Butler's label of left conservatism, but with big caveats.
What is 'identity politics'? Not a single concept to begin with.
The term identity politics is widely used throughout the social sciences and the humanities to describe phenomena as diverse as multiculturalism, the women's movement, civil rights, lesbian and gay movements, separatist movements in Canada and Spain, and violent ethnic and nationalist conflict in postcolonial Africa and Asia, as well as in the formerly communist countries of Eastern Europe. The seeds of these partially overlapping conversations are apparent from the very first uses of the term identity politics in the scholarly journals. In 1979, Anspach first used the term identity politics to refer to activism by people with disabilities to transform both self- and societal conceptions of people with disabilities. Over the next decade, only three scholarly journal articles employed the term identity politics in their abstracts, to describe (a) ethnicity as a contemporary form of politics (Ross 1982); (b) a form of critical pedagogy that links social structure with the insights of poststructuralism regarding the nature of subjectivity, while incorporating a Marxist commitment to politics (Bromley 1989); and (c) general efforts by status-based movements to foster and explore the cultural identity of members (Connolly 1990). By the mid-1990s, references to identity politics as violent ethnic conflict (Meznaric 1993), and nationalism more generally (Alund 1995), emerged.
–– Mary Bernstein: "Identity Politics", Annual Review of Sociology, Vol. 31:47-74 (Volume publication date 11 August 2005). Reading order of the day!
According to this categorisation, there seems to be a widespread conflation of meaning b and c, assuming an analytical or even revolutionary marxist connection from b where there is only a mildly reformist and progressive conservative aspect in c.
So, how to name that baby?
While we are sympathetic to these concerns, we believe the Left is now characterized by an excessive and destructive fragmentation that threatens to subvert any possibility of concerted, unified Left politics beyond the limited agenda of particular identity movements. In our view, this threatens the very essence of what has constituted the best tradition of the Left, that capacity to advance a universal vision of solidarity and justice that builds and depends on pluralistic social movements but transcends their own particularistic agendas. We thus propose a dialogue about a common agenda that might unite all sectors of the Left and about the directions of change necessary not only in the larger society but in the Left itself.
–– Charles Derber & Karen Marie Ferroggiaro: "What's left? Radical Politics in the Postcommunist Era", University of Massachusetts Press, 1995.
In the political philosophy of multiculturalism, ideas are focused on the ways in which societies are either believed to or should, respond to cultural and religious differences. It is often associated with "identity politics", "the politics of difference", and "the politics of recognition". It is also a matter of economic interests and political power. In more recent times political multiculturalist ideologies have been expanding in their use to include and define disadvantaged groups such as African Americans, LGBT, with arguments often focusing on ethnic and religious minorities, minority nations, indigenous peoples and even the disabled. It is within this context in which the term is most commonly understood and the broadness and scope of the definition, as well as its practical use, has been the subject of serious debate.
–– Wikipedia: Multiculturalism
So what does identity politics have to do with the Left? Let me state firmly what should not need restating. The political project of the Left is universalist: it is for all human beings. However we interpret the words, it isn’t liberty for shareholders or blacks, but for everybody. It isn’t equality for all members of the Garrick Club or the handicapped, but for everybody. It is not fraternity only for old Etonians or gays, but for everybody. And identity politics is essentially not for everybody but for the members of a specific group only. This is perfectly evident in the case of ethnic or nationalist movements. Zionist Jewish nationalism, whether we sympathize with it or not, is exclusively about Jews, and hang—or rather bomb—the rest. All nationalisms are. The nationalist claim that they are for everyone’s right to self-determination is bogus.
That is why the Left cannot base itself on identity politics. It has a wider agenda. For the Left, Ireland was, historically, one, but only one, out of the many exploited, oppressed and victimized sets of human beings for which it fought. For the ira kind of nationalism, the Left was, and is, only one possible ally in the fight for its objectives in certain situations. In others it was ready to bid for the support of Hitler as some of its leaders did during World War ii. And this applies to every group which makes identity politics its foundation, ethnic or otherwise.
–– Eric Hobsbawm: "Identity Politics and the Left", new left review, 1996.
These suggestions all have a not so slight potential to be read as "non-neutral", even potentially offensive. But "left" is that already as well in many ears. Or would be.
Identity politics is not a left movement per se. The identarianist movement is the prime witness for that. If t is still to be called 'left', then it one has to do even more explaining to do than for the above words.
Like for example the esoteric usage here, for 'Left Conservatists':
Mailer has continued to use the label ("Left conservative", for instance here), though in a rather idiosyncratic way. Basically, he wants to be an egalitarian, but he doesn't want to be a liberal, because liberalism simply isn't compatible, in his thinking, with "family, home, faith, hard work, duty, allegiance" and other "dependable human virtues," to say nothing of Mailer's belief in God and the Devil. But he can't be some sort of "compassionate conservative," because the folks that coined that term have turned out to be "flag conservatives": people who, according to Mailer, don't believe in living out American ideals so much as reifying them and turning them into something that can be served by military might, something that can be imposed by force. So he sticks with "left conservative," though he allows he has to constantly explain that description to everyone who asks about it.
What Arac calls the "blurriness" of Bell's argument helps explain, though it does not justify, the subsequent phrase "left conservatism." In leaving out the word cultural-a more precise alternative would have been "cultural conservatives on the Left"--this condensed formulation makes the absent term into the sole arbiter of political identity. The intent behind the phrase may be only to suggest an inconsistency: leftist in one domain, conservative in another. But the noun conservatism, having ingested the invisible modifier cultural, lords it over the remaining modifier left. The effect is to insinuate that the final or fundamental political identity of the person so described is conservative. A cultural conservative, even on the Left, thus stands accused of no longer being a leftist at all. […]
Unfortunately, the same "everything-is-culture" equation underlies the widespread confidence that if one is progressive in matters of culture, one is a progressive, period. The asymmetrical arrangement of noun and adjective in the phrase "cultural Left," which need not be a piece of sarcasm (I use it straight, for instance, in the paragraph above), encourages us to assume that leftist political identity can be firm and substantial even though it is restricted to culture, in other words, unsupported by any taking of sides in matters of economics or politics in the strict sense. If that phrase does not suggest a leftism only in the domain of culture, a possible and more humbling interpretation, then it could certainly be seen as a form of self-flattery. Surely it makes no more sense to allow one's position on culture to dictate political identity than it made, once upon a time, to allow that identity to be read off exclusively from a position on the falling rate of profit or the utility of electoral politics.
–– Bruce Robbins: "Disjoining the Left: Cultural Contradictions of Anticapitalism", boundary 2, Vol. 26, No. 3 (Autumn, 1999), pp. 29-38.