When I run 24VAC into a full wave bridge rectifier followed by a 220uF electrolytic capacitor to turn it into ~32VDC, the source has two wires. Does it matter in what order I connect the AC wires to the input to the bridge rectifier? If so how do I determine which wire goes where? I suspect that it's totally symmetric on the input side, but I'm am full of doubt when it comes to AC. Sorry if this is just a really dumb question.
As long as you are dealing with a closed system (like a transformer secondary winding + bridge rectifier) then no, AC is not polarized.
However, when dealing with outside power (like what comes out of the wall) we do consider AC-carrying cables to be "polarized". There's the hot wire carrying the juice and the neutral wire carrying the return. The hot wire should go directly to your device's switch / fuse, and any semi-exposed contacts must have the hot wire as protected as possible. If you don't do this on production items you will fail UL certification and be wide open for lawsuits. The common light bulb would likely fail many of today's standards, but it's been around too long to recall.
Devices that don't have a polarized wall plug will use a double-pole power switch to prevent the circuit being live up to the switch.
At the atomic level, with the AC coming out of your transformer there is a herd of electrons which all run one way, then stop, turn round and run the other way half a cycle later. Since the electrons are running in both directions the transformer output has no polarity. The job of the rectifier is to round them up and make them all run in the same direction. Now you know which way they're going they now have polarity. That's why the input of the rectifier doesn't specify which way round to connect the wires, but the output does.
For your AC/DC application, the polarity won't make a difference in how it functions, but it's important to understand, in case we're generalizing, that POLARITY MATTERS in hot/neutral circuits in the U.S. [and some other countries] WHY? Because most lamps and other devices with on/off switches are only opening/closing the contacts connecting the HOT wire, and are leaving the NEUTRAL WIRE connected the whole time, so if HOT/NEUTRAL get reversed in the wall outlet, then the lamp's switch is switching on/off the NEUTRAL (instead of the HOT), which means that the light bulb terminal is STILL HOT! when you turn off the light to change the bulb, and you can get the shock of your life if you touch it, and your body happens to be able to complete the circuit to ground. SO, PLEASE make sure your wall outlets are wired correctly.