I've heard that safety polypropylene capacitors are recommended for filtering high-frequency noise from switching components
It's rather hard to have an argument with hearsay.
The capacitor you have is rated to be connected across the line voltage of up to 240VAC. So it'd be connected directly across the primary terminals of the transformer.
The diagram of the secondary you have shown will not work. The best you can get is one supply (positive or negative):
simulate this circuit – Schematic created using CircuitLab
Quite a bit of switching noise comes from the rectifier diodes on the secondary side of the transformer. You need to use fast types - e.g. UF4001..4007 to minimize that. The "standard" 1N400x rectifiers perform much worse, since they take much more charge to turn off compared to the ultrafast UF400x. That means that after the secondary voltage has fallen below the capacitor voltage, the rectifier conducts too long and discharges the capacitor back into the transformer for a little bit. This builds up the secondary current. Eventually the rectifier turns off and the transformer secondary generates a voltage spike as the current collapses. That's not good, and it's oft overlooked in audio designs. The ultrafast rectifiers will turns off much quicker, and the residual turn-off current in the secondary will be much smaller.
To get symmetric supplies you need a half-bridge rectifier with a single secondary:
simulate this circuit
Or you need a full bridge with a tapped secondary:
simulate this circuit
You also should have a power switch and a fuse on the primary side of the transformer. Never skip those two.