When measuring conformism, of course, you have to say with respect to what, and this changes as kids get older. For younger kids it's the rules set by adults. But as kids get older, the source of rules becomes their peers. So a pack of teenagers who all flout school rules in the same way are not independent-minded; rather the opposite.
Since one's quadrant depends more on one's personality than the nature of the rules, most people would occupy the same quadrant even if they'd grown up in a quite different society.
I think these statements contradict each other. On the one hand, the source of rules to which you are conformist or independent depend on your peers — your social context, if I may — and on the other, your "conformist—independent identity" is somehow independent of that society? Unless the claim is more that people sort themselves into social circles based on their alignment. But in that case, the customs protecting free inquiry haven't been weakened; Paul Graham has just accidentally sorted himself into a conventionally-minded circle.
Instead, I'd claim that one's alignment on this chart can vary significantly based on their social context. I find that I've shifted from "passively independent" to "actively independent" towards my parents as I've matured and become independent from them. In my research lab, I am pretty comfortable staking strong opinions and disagreeing with my advisor on technical issues, but when the topic is about what I need to do and when I need to do it by, I am much quieter as I'm her student and she holds that power over me.
Further, vocal support by active independents for social norms that allow independence of thought might look a lot like active conformism. And, perhaps it is, since one's "conformist—independent identity" depends on those social norms! But that doesn't mean that those advocates otherwise make active conformist choices.
Since Paul left the exact social context he's thinking in vague, I can't really say a lot more about what he's thinking about. I will say that the situation at universities is complex; administration has taken a lot of power from faculty, but perhaps those faculty have been hoisted by the petard of their independence, which makes cooperation difficult at times and prevents them from using their power effectively. (Leaving aside the possibility that PG is instead discussing the situation of assholes being allowed to be assholes, as nobody ought to defend that position.)