Staying home with one's kids is a totally valid choice. And lots of people want a card to hand out. So it's easy to see how "the Mommy Card" must have seemed like a great idea to whoever had the brainstorm.
And it is a perfectly good idea — to the extent that anyone without a formal affiliation might want a card. I myself had plain old cards as a freelancer, and found it a useful way to hand out information. But here's where they get weird. These cards don't just have the mom's name and info on them. Rather, they say "mom to Poppy and Otis" or whatever the names in question might be. On the one hand, this probably makes a lot of sense since this is actually how a lot of moms know each other, and it's probably just the most practical way to identify someone whom you've met on the playground or at Gymboree when your kids hit it off. But on the other, from an identity perspective, it could be...problematic for a lot of women. One such is the blogger MarsIAm, who wrote (after receiving the offer of a pack of such cards),
Maybe this is a feminist thing, or maybe it's because I'm not a mother, but even if I was a stay-at-home mom with no job (and therefore no reason to already have business cards) I wouldn't extol my ability to wipe snotty noses and read bedtime stories as a core part of my persona. As if your main accomplishment is childbirth, and you would like to commemorate your skills with a card detailing your contact info after the names of your offspring. To provide to other moms when you need to carpool, or if they want your ants on a log recipe.
My own mother was a stay-at-home mom (although she abhorred the expression) and I think she would have seen being a mother as a key part of her persona, and something she was proud of. (She also had other people call her much more often for her analysis of Schopenhauer or her opinion on politics than for recipes or carpool questions, for that matter.) But when I asked her, she too found these cards odd. "It's always problematic to base your identity on someone else," she said definitively. "And that's a lot of pressure on the kids. But I'll tell you who it would be good for: the mother of the bully. So you know who to call when he beats your kid up or steals her bike. You'd know exactly who was responsible."