Why don't my LED Christmas Lights change color at the same rate
Manufacturing tolerances, plain and simple.  

Every part is made with a tolerance.  A 100 ohm resistor, 5%, is between 95 ohms and 105 ohms.  

Obviously that is affecting the timing of the various lights.  

They are built with a simple timer circuit such as a 555, that relies on a resistor and capacitor, and is therefore subject to the manufacturing tolerances of both, as well as itself. They do not pick up the AC heartbeat, because that would add to the cost of the bulb, I guess. And then you wouldn't buy it.