I would not get upset at someone else's parents giving their child a birthday card on their child's birthday. It is not about you. Perhaps if I had been your SO I would have complained about their giving him a type of card he asked not to receive on his birthday but it does not sound like he did that.

Too, that your SO used you as an "reason" not to be given a card like that is bad behavior on his part; he gets to send/receive any kind of card he wants for his own reasons; no one was giving you a card so what you like/do not like has nothing to do with anything. That they made a joke of "don't show beauflow", especially after your SO gave them the gratuitous, personal information about your likes and dislikes (instead of his own) is very rude but, fortunately, they are not your parents so you do not have to deal with them, they're your SO's problem all the way.

I would shrug and realize I don't like these people very much, don't ever want to hang out with them when I don't have to.