Would you accept being told that the store wouldn't be able to accept your return then? Of course you'd be perfectly in your right not to provide personal info, but the places I have worked wouldn't be allowed to take your return without it.
For me it would depend on how well the store made that policy clear before I purchased the item. It doesn't need to be posted on the wall in three foot high blinking letters, but it can't be hidden on the wall in the employee's only break room, either. Most places seem to put the return policy near the register and on the receipt. If that's the case, and it specifically says you can't return cash purchases without giving personal information, I'd consider myself fairly warned.