Actually Wal-Mart appears to be less interested in data-mining you than are big grocers like Kroger, Ralph's, Safeway etc. You don't need a loyalty card to get Wal-Mart's best prices on groceries.
While Wal-Mart could theoretically match your purchases with your debit card data, and maybe they do, you're welcome to pay cash and be anonymous. Compare with the many grocery chains that require you to pay a significant premium for anonymity (i.e. they require the use of loyalty cards to get anywhere near reasonable prices).