Does A Dance with Dragons movement reduction rules affects Shift too?

NO

NO, it simply reduce the movement to 2. Charge rolls, Shifts, Retreat rolls ecc... are not affected.

Example :
You roll a die for the charge and add the die to the movement you have (2 in most cases, bog and hidden traps can lower it more...)

You shift 3" with tactical reposition.

You shift 2" before a ranged attack.