OK, I spent a little more time looking into this and I think I understand what's happening. A standard diode will pass current in the forward bias direction, but there will be a voltage drop of 0.5V-0.7V across the diode. In the opposite (reverse bias) direction, no current will pass through it so the voltage drop will be whatever voltage you apply to it.
My DMM (and I suspect many others) only generates a voltage of about 1.35V to test a diode. So when I use it to check a standard diode, I get 0.5V in the FB direction and 1.35V in the RB direction. This is correct.
In the case of the ABS sensors, the various forum posts indicate that there should be about 2V in the FB direction and "OL" in the RB direction. I'm not sure what OL means, but a RB diode should have a voltage reading that matches whatever source is applied, unless the voltage exceeds the breakdown threshold (which usually damages the diode).
Back to the expected reading of ~2V... That can only happen if there are 3 or 4 diodes in series (so the sum of the voltages across each diode adds up to ~2V) or if there is also a resistor in series with the diode, in which case the voltage will depend entirely upon how much current the DMM is pushing through the circuit (V = IR + ~0.7V). That current will very likely vary from one DMM to another, so it may not be correct to state that a reading of 2.0xxV is the only valid reading.
In either case, my DMM doesn't generate a voltage that is high enough to forward bias the diode (or diodes) so I'm getting 1.35V in both directions on all sensors.
The bottom line is that the DMM has to generate a test voltage that is well above the expected 2V reading or it won't work. So I'm going to try to get my hands on a DMM that can do this.