The titles (which grammatically are appositions)
Appositions are something entirely different. Everything you said afterward is invalid.

If you mean that those identities can't coexist in one person, I don't think you are right. There is an idea of possible worlds (suggested by Leibnitz) which in one of its reading says that a person lives in different possible worlds: in one he is a father, in the second he is a teacher, in the third he is a son, in the fourth he is a husband, in the fifth he is a customer, in the sixth he is a lover etc. These epitomes don't exist simultaneously, one of them surfaces at a given moment (say, when you are spending time with your kids your are a father), while others "stand by". When you come to the office you stop being a father and your CEO epitome switches on. Curiously, different epitomes can be axiologically different - one may be a good CEO, but a bad father, a pleasant customer, but a horrible husband.

If we adopt this approach, the different identities you speak of may not be mutually exclusive - one can be a patriotic feministic nerd who is a connoisseur in pervert games.
What I was saying is that we are presently going through a period in which identity partisanship is intense in magnitude at the same time as there is a proliferation of identities that are similar in cultural importance and influence. What this means is that these identities, especially ones that explicitly conflict with each other, cannot settle easily into equilibrium as they are all too forceful with respect to each other. Furthermore, all of these identities are internally-riven with internecine contest over fundamentals. The world has never been more pluralistic, but the space for identities is too crowded, similarly to typical cases involving population groups/political units.

Think of how many cases we have today of Identity A partisans engaging in a vocal and public, even existential, struggle against partisans of other identities that they consider to be infringing or threatening their broad worldviews and ways of life. These identities are all very powerful in historical terms due to the confluence of population growth (i.e. more partisans), technological innovation (i.e. higher capacity to grow the identity convergently, divergently, or against other identities), and capitalist economics promoting an amenable environment (i.e. labor binds all identities together and lubricates the fault lines). On the other hand, partisans cannot find resolution as opposing identities are comparably powerful in the immediate circumstances. Identities do compete with each other (both within and across individuals), but multiple similarly-strong forces grinding against each other builds tension, so to put it simply we have:

1. Many identities
2. Many partisans
3. Limited capacity for identities in the current environment to dominate or decisively overwhelm each other.

So fear, anger, and other passion will continue to build up. Since the world wars powerful states have generally outsourced many of their powers to multinational corporations, and in return the corporations created an economic framework in which nations and states had incentive to focus on production and service above all else. Thus we see some people claiming that we have seen an unprecedented and perhaps permanent decline in violence and warfare. However, the modern economic framework has become badly frayed and people are left to focus on their identity partisanship and resistance against perceived hostile identities. An obvious outlet of that would be into nationalism and parochialism in general. Moreover, since it would be challenging for the economic and political orders to both recover and assuage tension between identities, the trend is really toward a 'meltdown' and subsequent stabilization. The most simplistic interpretation would be armed ethnic conflict leading to another round of large-scale wars in Europe and elsewhere, but the whole issue is further complicated by the fact that we cannot even begin to factor in the inevitable disruptive effects of climate change and new technologies...

I'm not going to comment on this thesis in the thread anymore - it's making me wince to read it.