MadEngineer:

 

The most annoying thing is that although I can pay by presenting my wallet to the machine I still have to present the loyalty card.  

 

You don't have to use loyalty cards at all.  It's up to you. 

Someone I know well has a second wallet just for all their 'loyalty' cards and this doubles the length of every transaction. 

With a very small number of exceptions I don't use them.