Look for another identifier besides color such as a stripe or rib on one of the two other wires. That will be the Neutral wire. Make sure it connects to the Wide blade on the plug.
Is this because it is AC? No, if it isn't so identified, you are dealing with a cheap knockoff pigtail that probably belongs in the waste bin. In the 120V single phase world, Neutral is effectively at ground potential, therefore if you touch it, you shouldn't get shocked. Hot while alternating isn't at ground potential and so the voltage is alternating between +120V and -120V (RMS, actual voltage peak ±170V), making you the conductor if you connect the hot wire to the dishwasher chassis and you touch it and ground. If the neutral connects to ground in the dishwasher, you've just connected up a dead short.
As this is for a dishwasher, neutral must connect to neutral and hot to hot, any mess-up here is going to be ugly. The only other method is to use an ohmmeter to trace which wire is attached to which blade. Normally narrow blade hot, wide blade neutral and ground pin to ground. If there is no difference in blade widths, then use the socket chart below to figure out which blade is Hot and Neutral from its position and attach the wire to the appropriate terminal in the appliance.
There is only one instance where the connections could be considered even remotely "interchangeable" and that is on a double insulated device where neutral is totally and completely isolated from ground.
NEMA socket listing with blade width and "polarity". Note that NEMA 5-15 and 5-20 can be installed with the ground prong up (coat hanger excluder mode) so right and left slot position is relative.
National Electrical Code 2014
Chapter 4 Equipment for General Use
Article 400 Flexible Cords and Cables
II. Construction Specifications
400.22 Grounded-Conductor Identification. One conductor of flexible cords that is intended to be used as a grounded circuit conductor shall have a continuous marker that readily distinguishes it from the other conductor or conductors. The identification shall consist of one of the methods indicated in 400.22(A) through (F).
(A) Colored Braid. A braid finished to show a white or gray color and the braid on the other conductor or conductors finished to show a readily distinguishable solid color or colors.
(B) Tracer in Braid. A tracer in a braid of any color contrasting with that of the braid and no tracer in the braid of the other conductor or conductors. No tracer shall be used in the braid of any conductor of a flexible cord that contains a conductor having a braid finished to show white or gray.
(C) Colored Insulation. A white or gray insulation on one conductor and insulation of a readily distinguishable color or colors on the other conductor or conductors for cords having no braids on the individual conductors. For jacketed cords furnished with appliances, one conductor having its insulation colored light blue, with the other conductors having their insulation of a readily distinguishable color other than white or gray.
(D) Colored Separator. A white or gray separator on one conductor and a separator of a readily distinguishable solid color on the other conductor or conductors of cords having insulation on the individual conductors integral with the jacket.
(E) Tinned Conductors. One conductor having the individual strands tinned and the other conductor or conductors having the individual strands untinned for cords having insulation on the individual conductors integral with the jacket.
(F) Surface Marking. One or more ridges, grooves, or white stripes located on the exterior of the cord so as to identify one conductor for cords having insulation on the individual conductors integral with the jacket.
That kind of T-connection low down suggests that it joins the wastes from two P-traps.
It is probably more usual for dishwashers to connect above the P-trap of an adjacent sink.
An "appliance P-trap", the tapered nozzle on the left is to connect the outlet hose from an appliance such as a dishwasher.
You can also get a "standpipe appliance trap"
I've not used this type but your appliance hose would be hooked into the top.
If you can remove one of the outlets that your T-joint combines then you might be able to plan a new layout for the waste pipes that provides more space for your appliance.
It isn't clear to me from your photo, exactly what the problem is and what exactly feed the two inputs to that T-join.
In principle you can cut through the pipes and push on a new solvent-weld (or push-fit or compression fitting) joint. But you need enough pipe remaining after the cut to fit into the coupling. The more times you cut and remake these solvent-weld joints the less and less pipe you have to work with.
As you suggest, if there is nothing using the vertical waste pipe above the T, you could cut out the T and cut back the existing pipe far enough to fit a new section of the same type of ABS pipe with two straight couplings.
Best Answer
In general, connectors like that are classified based on the pin thickness and pin spacing. That might cut your solution set from a million connector models down to a few hundred thousand: useful but hardly solving the issue.
Posting photos of the far side of this connector would help also. Major vendors love to make one off connector designs so nothing else will fit. In which case you're out of luck, short of finding a used connector harness, or scavenging similar models at a dump. Sometimes you can get lucky and the only difference is a keying pin (like the plastic bumps at the top of your photo). Then you just cut off the keying feature and run with it.
If it were my washer, I'd probably saw open the failed connector, solder the wires directly to the pins, gently insert bare pins into the valve, and seal it all up with an appropriate clear silicon caulk (clear so I can see if anything goes wrong).