When looking at the customers profile page you can turn off various commutations preferences for a customer for both Email and SMS messages. 

If you turn off SMS messaging for the customer, when you look at the Email and SMS panel on a customers booking you will be unable to send the customer SMS messages.

On the online system when setting up an account for EU customers can choose what communication preferences they wish to receive, and after they have registered the can update their communication preferences at will.