I have an audio circuit, from ESP. I've built this, it works. But C1 and C7 seem backwards to me, why does the audio signal go from - to +?


Here the audio signal goes from + to - in C5 and C6, that makes sense to me.

 

Capacitor polarity has nothing to do with signal direction.
It is determined by the DC bias voltage on the capacitor. You want to avoid having the capacitor reverse biased. With AC signal, reverse bias is unavoidable.

 

You don't show the power supplies. I presume that as these are derived from professional equipment then they are probably running from ±15V supplies. That being the case, the signal is centred about 0V throughout and the only need for capacitive coupling is to remove any DC that accumulates due to amplification of the offset voltages of the op-amp.
For a JFET op-amp the input currents are negligible and don't contribute to the DC offset.
The datasheet says that the offset can be ±4mV, so it is equally likely that it could be positive or negative, so the orientation of a polarised electrolytic is a random choice. In an ideal world, one would use a non-polarised electrolytic, but they cost a few pence more.