I voted "it depends" because I'm close enough to a very few people that personal questions are okay both ways.
But in general, Imo any question that involves someone's money can easily be considered rude and that would definitely include diamond specs. I just say "Ooh, that's pretty" when shown a diamond ring and let them elaborate or not as they choose.
Now and then someone over-asks about my rings. I think they are usually just a little clueless but mean to be friendly. If I don't want know them or don't want them to know my business and they ask if it's real I might say no (though it is) and if they ask how big it is I might say I don't know. It seems nicer than saying "None of your own business."
I had a pretty interesting experience when visiting a very well known high jewelry shop in Paris. Our SA asked how many carats my ring was, and continued to guess carat size even after I tried to change the subject and telling her that I don’t know. Unfortunately it didn’t stop there. She then decided to ask how long my partner and I had been married. Needless to say I left without making any purchase.
Never asked anyone, except only one or two of my closest friends, and they love jewelry. Even so, I feel awkward to start the conversation.
But hopefully in the near future, when the PS get together is back, i will definitely join and ask you guys ALL the details, EVERYTHING! I won't be shy.