Ah, now I see what you mean. Multiplication could have been defined so that it is not commutative. And indeed, matrix multiplication is not.
On the other hand, primality appears to be an intrinsic property of the integer seven. I cannot imagine how one could "redefine" seven to make it composite. (Unless one wanted to redefine multiplication to make that true.)
Still, I have my doubts. As Kronecker said, "God created the whole numbers; everything else was man's handiwork." Integers suffice if all we are going to do is count things. However, if we also want to measure things, we need more sophisticated mathematics. And the further we get from the integers, the more formalism is found in our mathematics. Thus we decide that multiplication of scalars is to be commutative, because it is more useful that way.
When I said that reality is more fundamental than mathematics, I was thinking that nature is always richer in detail than our mathematics. Mathematical modeling is difficult; invariably, we are forced to omit things from our models. Even the "laws" of physics turn out to be, on closer examination, merely good approximations.