I'm annoyed with people that give christmas cards
Is there something else you want in the christmas card?
I don't want anything in christmas cards, people just send you what they want to send you.
It is understandable not wanting Christmas cards for other people. But you should not be angry at them for a traditional custom. It is irrational and selfish to be annoyed with others who are being nice.
I am not giving christmas cards back because I don't want to deal with these people.
That is okay, you do not need to reciprocate. You can also just be honest and tell them that you no longer wish to receive them.