XOR is not a great choice here. Consider that 2 copies of a row give the same result as 0 (or 4, 6, etc). And even without multiple copies of rows, you can force any hash you'd like by observing what happens when you insert more random rows and finding a subcollection that flips exactly the bits you want.

What you probably want to look at is homomorphic hashing. This is usually implemented by hashing each row to an element of an appropriate abelian group and then using the group operation to combine them.

With suitable choice of group, this hash can have cryptographic strength. Some interesting choices here are lattices (LtHash), elliptic curves (ECMH), multiplicative groups (MuHash).