One thing is it's all relative.

When "aero" first became popular (early 80s), the Araya ADX-4 was considered "aero". Today it'd be considered a very small non-aero rim. I'm guessing it was 25mm tall, give or take. If you used oval spokes then you were really cutting edge.

I got soundly criticized for using an oval spoked ADX-4 front wheel at a crit one year - "too dangerous" "are you an idiot?" etc. Now it's normal to use 60-90mm tall front wheels on the same course, even when it's relatively windy.

So for me, I get uneasy at about the 58-60mm rim height in gusty winds where I'm hitting 50 mph. 45 mph, 60mm is fine. 50 mph, not so fine.

My "non aero" rims are HEDs and probably just slightly under 30mm tall, and they have oval spokes up front I think. To me they're "non-aero" and not affected by wind.

Incidentally this all has to do with the front wheel. The front wheel turns slightly in heavy wind and puts you slightly off balance (since, by definition, you balance a bike by making small steering inputs).

A tall rear wheel stabilizes you - I've paired a disk rear with a non-aero front, or disk + trispoke (Specialized TriSpoke aka HED3) front, in pretty windy conditions in tight crits. A 90mm rim in back (Jet9) with the non-aero front is extremely stable.

*edit* there's yet another factor. "Aero" doesn't necessarily mean "affected by crosswinds". Apparently the Stinger6 is pretty tame in crosswinds (and here I was thinking I was a good bike handler). Other similar height wheels can be harder to handle. So a Zipp 101 wheel, for example, may test well for aerodynamics and still be relatively unaffected by crosswinds.