Well, since it seems to be a question of desecration, I guess I'll chime in:
1.) If the proper rules of detecting are followed (filling your holes, picking up visible trash, leaving no sign you were there, etc.) then there is no vandalism or desecration. We're not talking about grave robbing or digging for items buried with the deceased. One would be looking for items that were dropped by the living. Is a Barber dime that falls from a pocket in a cemetary and more sacred than one that falls in a park?
2.) Of course one should not detect in an "active" graveyard. Not because of some mumbo-jumbo about it being holy ground, but because it would make the mourners feel uncomfortable. In long defunct cemetaries, where the grandchildren of the ones buried are long dead, your only obligation is to not vandalize and not disturb the graves themselves. Christians themselves speak of "ashes to ashes, dust to dust"... the physical part of a person returns to the ground, while the soul travels beyond. Coins and such are not part of the spirit world, they're minted for the use of the living.
3.) Today, at least, people buy their burial plots, making the area directly over the bodies PRIVATE PROPERTY... and since the owner CAN'T give permission, don't detect directly over graves.
4.) Local laws and the rules of public vs. private property still apply
5.) The idea of "what will people think" should be considered, but not be the final decision maker. Every place we detect is considered "inappropriate" by someone. Its part of the game. If I stopped hunting in every public place that someone said "should you be hunting here?", I'd have no place to go. If your in the right legally, it only comes down to how much scorn can you take. I personally could care less about what others think of me, and I'll let them know that to their faces.
So, given these factors, I'd say I have no moral problem detecting for dropped items in 1.) long abandoned cemetaries, on 2.) public land, if the 3.) law permits, in 4.) areas not immediately around the graves. But would I do it myself, probably not... only because there are plenty of other areas that are far less hassle.