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.