That’s employment in society’s eyes.

Well in reality stay at home parents are engaged in unpaid employment that is completely unrecognized (or recognized as Not in Labor Force).

>in society’s eyes

That’s all that really matters for many people.

Unrecognized by who? Unpaid? You are investing in the most valuable thing that exists. Is somebody else supposed to pay you to raise your own children?

There is increasingly an expectation that mothers will have a paying job. My wife is a stay-at-home mom and gets some strange reactions when sharing this (I just say it's way harder than my job).

Those people do not really seam mentally sound, and could be best ignored.

Lot's of people (like more than half the population we interact with) assume that my wife has a job, even knowing that we have four kids. I'm not sure your advice about ignoring all of them is sound...

Wouldn't be a terrible idea given the long-term benefit to society at large of having young, healthy, educated adults. A relative shortage of them is a serious concern for a number of societies around the world.

"Society at large" is more hostile to young, healthy, educated adults than ever. The first step is to reduce the leeching of these people, so that they can have families as is the natural order.

How so?

Depends which country you've taken your definition of NEET from.

In the UK, the classification is applied to people aged 16-24 (thus excluding the retired) and sometimes phrased as "respondents who were out of work or looking for a job, looking after children or family members, on unpaid holiday or traveling, sick or disabled, doing voluntary work or engaged in another unspecified activity"

On the other hand in Japan the NEET classification covers ages 15 and 34; and people who are engaged in housework or who are actively seeking work aren't considered NEETs.