The term was coined by Ken Rockwell, I believe (*). Basically, someone who is so absorbed in resolution charts, MTF curves, micro contrast, etc., that they never look at the photo as a whole, or maybe they spend $10,000 on equipment just to mostly photograph test charts. Show them a wonderful photo taken by HCB, and they'll pull out their loupe to examine the grain. They are the wankers you don't want to talk photography with.
Anyway - your original question is excellent and complex.
For my first 25 years in this hobby (35mm format), I didn't care about sharpness because the results I got, either printed from a lab or printed myself, were acceptably sharp. When I entered medium format (Hasselblad) and studied the Zone System, I became much more technical and obsessed over sharpness. I'd always use a tripod, always pre-release, I'd use films like Tech Pan, I'd print at 16x20, and so on. My photos were still good, but certainly I was also choosing subjects where I could demonstrate to myself the sharpness I could achieve.
That has since changed in that I can be happy with a photo that is good because of the subject, catching the right moment, the colors, composition, whatever. Sharpness has to be good enough, but doesn't have to be the most important thing.
I have been upset though when I get simple 4x6 or 5x7 prints from a lab that are so unsharp it's distracting. With the shift to digital, I believe the quality of lab prints have gone down.
(*) Yep:
http://www.kenrockwell.com/tech/7.htm