I believe one, and only one, thing will happen.
Some of those who do believe in the Mayan prophecy will
create mayhem, through their panic, for the rest of society...and that might be almost as bad as if the prophecy itself was fulfilled.
It doesn't take major catastrophic disaster to inflict utter chaos, it just takes enough people who believe that it's going to happen, particularly people in positions of authority. JMHO