This essay only works because Paul Graham is a white man in America, whose 'identity' is the presumed default in the society he lives in. Anything he makes a part of his identity, he gets to choose. If he chooses nothing, he has the luxury of being 'just normal' and gets to go through life thinking of himself as perfectly rational.
Sometimes you get to choose what you identify with. Other times, people choose for you. For instance, you don't get to wake up one morning and decide not to be black, or gay, or a woman. You don't get to simply shed those categories and avoid the increased violence that comes your way apropos of nothing.
I know, you're already thinking, "but this essay is about religion and politics!", but the thing is, for a lot of people, politics are not abstract.
I'm also a straight white cis guy living in America, and so I have the luxury of choosing or choosing not to support gay rights, or feminism, or racial justice. I can choose or choose not to make those things a part of my identity. In fact there's incentive for me to choose not to, because if the balance of power were re-arranged in society, and poverty and violence were more evenly distributed, my life might not be so easy.
But for a lot of people, making "politics" a part of their "identity" is a necessary defense mechanism, because the society we live in implicitly sanctions violence against anybody who shares characteristics of their identity they can't do anything about.
"Politics" is not some separate sphere you can disconnect yourself from. Politics are embedded in everything. Choosing not to "identify" with any political orientation is implicitly choosing society's defaults, and those defaults implicitly condone a specific power structure and make acceptable a certain amount of violence against certain people.