Are pull-up resistors needed for shift registers (constant current sink drivers)?
The output leakage spec when disabled is 1 μA max, so itself will not illuminate the LEDs. however this represents a high impedance condition [Mohm] which means it is susceptible to parasitic grid E fields for long strings acting as antenna and the diodes can rectify these AC fields into a small current.

if this is the case either a cap for DC CC not PWM or a pull-up R in the range to attenuate this stray field and at the same time remove the 1uA max induced voltage remaining on the cathode.  Use 100k to 10k typ. If you need.