"Sorry if it offends you, I just don't think in general that you should apply this stuff to society. Like... no."

I don't understand what "this stuff" refers to in this sentence and it is far from clear to me that your interpretation of what your friend said is correct.

I also don't think it's a good idea to take an axiomatic approach to something like social justice. This approach:

• primes you in the wrong direction about complexity of value (when you hear "axioms" you think maybe 5 or 6, not 5,000 or 6,000)
• risks falling prey to confusion about the meaning of words
• risks confusing terminal and instrumental values
• risks assigning empirical statements probability 1.

Edit: Also, a general comment. Suppose you think that the optimal algorithm for solving a problem is X. It does not follow that making your algorithm look more like X will make it a better algorithm. X may have many essential parts, and making your algorithm look more like X by imitating some but not all of its essential parts may make it much worse than it was initially. In fact, a reasonably efficient algorithm which is reasonably good at solving the problem may look nothing like X.

This is to say that at the end of the day, the main way you should be criticizing your friend's approach to social justice is based on its results, not based on aesthetic opinions you have about its structure.