This is particularly American sensibility about not drinking alcohol casually around children

Shockingly this will vary by family. Some families take their kids bar hopping while they drink to excess, some drink casually and not in excess, and some are sober around their kids, and some remain sober all the time. My wife grew up hanging out in bars with her parents biker friends and their kids. She learned to watch some of them and save the good homemade wine when someone was about to topple. I grew up with parents who would have a single drink with dinner one to two times a week and would avoid getting drunk (at least that I know of).

Personally, as a parent and living in an area with a strong alcohol culture and with alcoholic family members, I drink very rarely (the alcoholic family members really kill my desire to drink), and when I do I make sure we have more than enough adults available to parent and drive if needed. I also am very much a lightweight so there is no drinking without getting noticeably giggly and sloppy. My wife feels and acts similarly but is not a lightweight and can realistically drink one drink and be visibly unaffected.

I honestly think the OP is less about the presence of alcohol around children but more just calling out a wine mom as such