If you don't give them a credit/debit card, you won't be able to use MM+ to make purchases.
If you don't want them to use your name, you won't be able to get certain personalized experiences (there are several rumored ones, but nothing concrete, other than meet and greet characters could call guests by name)
If you opt out of MagicBand, certain experiences triggers by the RF transmitter in the MagicBand would not be available.
If you opt out of creating a My Disney Experience profile, you wouldn't be able to make FastPass+ advance selections - which might lock you out of getting anything for the headliners.
And if you opt-out completely from RFID (if that will even be possible), you won't be able to use the FastPass+ system at all - and although uncertain it seems unlikely that the original Fastpass system will remain.