The concept of "class," and especially class distinction rubs me the wrong way, but extending some minimum level of general respect and consideration with those you're sharing air with is another thing. You just don't see much of it any more.
We divide ourselves up into different classes, it's not like it's 1200 AD or 1920's India. You don't see wealthy elites rubbing elbows with 5th generation welfare mutts, do you? Neither one would feel comfortable. It's not a cultural thing, it happens across the spectrum of all kinds of people.
As far as being or having class, as in Cary Grant class, thats a whole 'nuther ball of wax. Any hope of "class" coming back kind of died with Madonna and Miley Cyrus or whoever the biggest super start tramps were before them. The days of "class" gave way to the days of "bling" and not much else.