Since the vaccination cards hold no ‘official’ status other than the CDC logo, there is little force of law to prevent copies other than copyright protection. Yes, the information can be cross-checked, but not easily.
So those who chose to vaccinate can just as easily participate in some Civil Disobedience by carrying multiple fakes along with their *real* vax card.
Gum up the system like the lady at the checkout line with a stack of credit cards. Declined? Here. Try this one
It IS a crime to duplicate that logo. So make sure you change it out. It’s small, no one is likely to notice. Use the MAD logo or something.