> It annoys my wife because she thinks I'm being rude
You are being rude. The innocent cashier is forced to ask you that question and has no power to change the rules. Why not be polite to them? If you really want to change things, try asking to speak to the manager (after you're done checking out, of course!).
How is not giving personal information rude? He is just telling them the truth that they don't need that information which is correct. If a cashier were to ask you your bra size would you be okay with it? Why is it okay to ask for phone number which will give you all that and more.
You are being rude. The innocent cashier is forced to ask you that question and has no power to change the rules. Why not be polite to them? If you really want to change things, try asking to speak to the manager (after you're done checking out, of course!).