Do people need to be at least 21 in the US with ID to buy cooking wine?
Well, I was getting some groceries at walmart once when I was 20, and got a bottle of cooking wine. I was not IDed (I remember because I realized as it was being rung up that it was alcohol and they probably weren’t going to let me buy it).
Yes you do.
I really don’t know if they card you when buying “cooking” wine, but the kind of “cooking” wine you buy in a supermarket isn’t very palatable, it normally contains salt and other additives. I think you’d get sick, before you got a buzz.
Most cooks don’t use cooking wine, the kind you can drink is preferable.
FWIW, I was not carded the several times I had to buy it when I was underage (and I definitely did not/do not look 21). This was in Indiana. Not “recognizing” that it’s alcohol is probably not an issue since most modern grocery store point-of-sale systems already have all alcohol products pre-programmed into the system and they prompt the cashier to check ID when they’re scanned. Apparently this did not occur when they scanned my cooking wine.
Cooking wine, as mentioned before, is pretty salty and rather unsuitable for drinking. I’m not sure where the line is drawn though or if there’s requirements for cooking wine and being 21… Just not in my experience though. 
Grocery stores that sell cooking wine don’t need a liquor license, so why should they card someone for buying something that, as stated earlier, is basically undrinkable?
I never knew this, thanks!