hhhmmmm, interesting topic. I have some time this morning so I am going to throw in my 2 cents.
Currently, prices for ABT tickets at the MET in the orchestra list at 85 bucks a pop

. IMHO if I pay 85 dollars to sit in a seat and watch a performance, I can do whatever I like when the curtain goes down. I have attended and performed MANY times in Europe and abroad so don't shovel that "everything is different in europe and outside the USA with respect" stuff to me. I can recall a Bejart piece being performed in Hamburg where the conductor came out before the performance began and verbally told the audience that he hoped they enojyed the show because in his opinion it was a piece of ***expletive deleted***. Lets talk about Pina Bausch in Vienna with the whole 'hair cutting thing", or how about Barishnikov in France doing the Kabuki thing that had people acting WAY less than cordial during the show and even demanding full refunds after. Oh yeah, there is always Nureyev being booed off the stage in Vancouver. Respect from an audience MUST be earned! Regardless of who is on the stage or what company is performing. It is not a god given right that if you dance on the stage that audience members who purchase tickets MUST embrace what you have choosen to do, even after the curtain has fallen. Now that being said, I personally don't think people should be rude during an actual performance but when the curtain falls and the dancing stops, anything past that is up to you as an audience member.
Now, here is another way to look at it. I am going to use myself as an example here
Right at the moment I am performing in NYC until July 9th. The show runs about two hours give or take a few minutes depending on audience applause

With an 8 o'clock opening curtain that puts the final curtain around 10:15. Now, because of where I am staying, out in New Jersey, the last train I can catch to get home leaves NYC at 10:52PM. That means, AS SOON AS THE CURTAIN FALLS I have to haul some serious booty to catch that train or I will be stuck in NYC

. I am almost certain that a percentage of all audience members in any given performance deal with the same scenario. It has nothing to do with respect but simply something that is out of your control. This is not a society issue, it is not an "American Thing", and it has nothing to do with a "decline in appreciation for dance", I mean hey, would you rather that people who leave during the applause not buy a ticket to come to the ballet? I know I wouldn't.