How can I achieve symmetrical analogue low-pass filtering?
The two filters have similar amplitude responses, but different phase responses. In other words, different harmonics of the original square wave are being delayed (phase shifted) by various amounts by the first filter, but they have a more nearly constant delay (linear phase shift) in the second filter.

While the two waveforms look very different on an oscilloscope, they do actually have essentially the same harmonic content, and will sound very similar if not identical to the ear. Human hearing is actually very insensitive to phase relationships of this sort.

It's relatively difficult to build linear-phase filters in the analog domain, while it's quite easy to do in the digital domain, particularly with an FIR filter. But you need to decide whether the results differ enough in your application in order to make the effort.