Math has no content, and I say this as someone with graduate mathematical training. Math is assume rules and see where they go. The rules that are useful in the day to day world are the ones we use day to day, not because they are some fundamental truth but because they are useful in the day to day world. It is true, there are other approaches, and they are perfectly valid math. Multiplication in the quaternions is not commutative, and multiplication in the octonions isn't even associative; non-Aristotlean logics uniformly lack the law of the excluded middle, and some lack the law of noncontradiction; and so on. For the programmers out there, think of SQL and its three-valued logic, and of how NaNs behave with relational operators. Different environments produce different mathematics.
In other day to day worlds, other mathematics would be appropriate; in this sense Western math is in fact culturist, because we have developed the day to day Western world and the day to day Western math together. Just because Aristotle said anything else was "repugnant" doesn't make it divine truth. We divide our thoughts into "hard" and "soft:" a mathematics that allowed contradictory statements to be simultaneously true would be useless in macroscopic physics and house building but very useful in human relationships and particle physics. One of these applications is not more "real" than the other, they are just different, and our preference for one regime rather than the other is cultural.
The question is actually, then, whether this is appropriate to teach K-12 rather than in graduate school. And that is _way_ above by pay grade.