Yes. the 100ms delays *should* mean the other port bits are stable at a valid logic level when the bit being manipulated switches. However if the PIC is exposed to a high level of EMI, that may not be the case. e.g. if there are long unscreened wires to the LEDs or tracks that correspond to a quarter wavelength in a GSM band and no groundplane. Without seeing the board layout and schematic (as Nusa requested), we are only guessing.
I wouldn't expect floating pins on unrelated ports to cause that sort of problem - its hard to conceive of a failure mechanism that could cause that sort of crosstalk on a different port other than severe ESD damage.
One possible issue that novices run into is failure to connect all the Gnd and Vdd pins. Combined with high currents drawn by the LEDs that could cause this sort of issue due to internal voltage drops across the die disturbing logic thresholds or gliching output latch bits..
I would suggest a simple test to eliminate gross hardware faults like pin to pin shorts. Tie /MCLR low to disable the PIC, forcing all its pins to be inputs, then jumper each port pin that controls a LED in turn to Vdd, through a 220R resistor for current limiting, and check that for each, only the correct LED lights.