Since the company that manufactures usually is different from the loyalty card provider, it’s probably safe to just take a screenshot of the loyalty app with the card being visible, and then just using that screenshot during checkout.
Even if you do not plan on actually cashing in on the benefits (which, if you shared the card, might be considered fraud), just presenting the card and creating random and unusable profiles could be a fun thing.
Personally, I would only consider using these screenshot for cash transactions, as credit card payments might be traced back to you.