Nope this doesn't sound right. I have a MIM that cancels noise fully with both pickups on, and doesn't have the out of phase sound.
I apologize.

I have been too short with my answer here. Allow me to go into a little more detail. In order for a standard jazz bass to archive a humbucking effect the pickups need to be RW/RP.
The RW part of that common pickup description mean Reverse Wound. This can be done one of two ways. Either "literally" wind one of the coils in the opposite direction of the first coil producing a clock wise and counter clockwise set of coils.
Or you can create a figuratively or "virtual" RW set as Fender does by simply winding both coils in the same direction but swap the leads so that black ground wire on coil one is connected to the start of the winding but the black ground wire is connected to the end of the winding on coil two.
Either of these scenarios will run the signal from one coil 180 degrees out of phase with the other coil. This mirror imaging of the signal (noise and all) is what cancels the 60 cycle hum. Neither method is superior as the signal doesn't care how it went backwards around the coil. It only cares that it
DID.
Now, the second half of our acronym stands for "Reverse Polarity" and is referring to the magnetic charge of the pickup. One pickup should have a
north pole facing the strings and the other should have the
south pole facing the strings. If your magnets are not reversed you will get a much thinner sounding tone with both pickups on. They will sound nice and full and perhaps even louder with only one pickup on.
This can be the case when two bridge pickups or two neck pickups are installed in the same J bass.
To check your stock Fender pickups first check the magnets because it's easy and we can do that without taking anything apart or buying any fancy tools
. To check the magnetic polarity of the pickups just hold a simple compass like this one next to the bridge pickup.
The needle should point either directly at it or directly away from it. Now move the compass up to the neck pickup. The needle should reverse direction quickly. If it pointed North at the bridge pickup it should point South at the neck pickup. If the Compass tells you that both pickups have the same magnetizing polarity then you have found your problem. You either have two of the same pickup (neck or bridge) or the magnets were installed incorrectly on the line.
I suspect the former.
Now, let's check the windings. Loosen the strings and remove the 4 screws that hold the pickup in. Now be careful here. Lift the pickup out of the cavity enough to see which side of the bobbin the black wire is soldered too. Are the colors on the neck pickup opposite of the bridge pickup like this?
They should be. If they aren't than you have two of the same pickup and you need to swap one out for the proper one.