ABS works as designed as long as a part time 4WD vehicle stays in 2WD mode. In 2WD all 4 wheels are able to rotate at different speeds (made possible by the differentials) and more importantly in 2WD both axles are allowed to turn at different speeds because only one drive shaft feeds rpm and torque to one axle.
As soon as you shift into part time 4WD (find out which kind of 4WD you have) both drive shafts become connected inside the transfer case and both axles are forced to turn at the same speed. More importantly, when stopping both axles will be slowed down at the same rate (any brake proportioning will be out of force) and the ABS system would get confused. After all, the ABS's job is to detect variations in wheel speeds and act accordingly. ABS will not function properly on part time 4WD systems!
Because part time 4WD and ABS do not mix, most manufacturers offered only rear wheel ABS on these vehicles since the rear axle needs ABS the most, due to the tendency to lock up first.
Some manufacturers saved the money and did not offer ABS at all on part time 4WD. On some vehicles a warning will flash that ABS is not working properly when in part time 4WD (Mercedes G-Class) - others offer no warning and the familiar pulsating of the brake pedal indicates that ABS is working . Well, its not.
However, on dirt roads and other off-road situations ABS could be bad for you and it should be "off" anyway. Read more...
ABS works really well with full time 4WD, AWD and automatic AWD.
However, it works only as long as the center differential of a full time 4WD is not locked. Locking the center differential turns full time 4WD into part time 4WD.
A word of caution. Some vehicles combine 4WD systems (could be full time plus part time - could be automatic AWD plus part time, etc.) On these vehicles it is your responsibility to know which setting to use (full time 4WD or AWD should is best for every day driving) and to know that once you select part time, ABS is compromised. Unfortunately, most do not have in dash warning about the non functioning ABS.
Jeep is a prominent example. The newer Grand Cherokees have automatic AWD. Both ABS and ESC work perfectly. In high range that is. Once you shift into low range the systems turns into a part time 4WD. In this setting ABS and ESC are out of force. And no warning is flashing to remind you of that fact.
It is possible that Jeep assumes that you know what you are doing. Know that ABS is no longer there for you. Since low range is a dedicated off-road setting.
ABS is not wanted by well versed drivers when off-road anyway.