Finite-symmetric-difference colouring of infinite subsets

Choose a representative $R$ of each class of countably infinite sets modulo finite symmetric difference, and colour $A$ by the parity of $|A△R|$. Removing one element stays in the same class and flips the parity. Every infinite candidate homogeneous set therefore has two countably infinite subsets of opposite colours. With choice, this refutes unrestricted countably infinite-arity positive partition relations on every infinite cardinal.