Check that the diodes are correctly placed across the relay coil !, with the ring end connected to the positive of your switched supply... if you find there the wrong way around, and are IN4148 type, replace them.
Otherwise, you could try and place a capacitor across each relay coil, a value between 1 Mfd to 47 Mfd with the diode, again positive end of the cap + to the power supply side; also place a series resistor in-line to the relay positive coil end, with a value between 10 to 22 ohms... this will depend on the relay pull-in working voltage, but is a good starting point.
If none of this helps, then it's likely the signal line inputs are at a charge level; e.g. your equipment in-out line capacitors have a DC charge, at each internal equipments blocking capacitor... by switching this potential to ground, will then discharge the in-out cap voltage, thus your popping.
The problem might be somewhat hard to resolve; mainly because you need to bleed away the DC potential build-up to ground, before you hard switch them. Adding a resistor on the in-put and out-put line feeds to ground, may reduce or remove the problem ?. So when your relay switch comes-in, the caps are near to ground reference potential, instead of floating between coupling potentials; particularly if there not internally, impedance terminated.
If your studio system is based on 600 ohm impedance, then a 1K2 value should do, placed on the in and out lines, e.g. between your relay contacts equipment in and out line connections... however, if the studio is based on 47K impedance, then terminate with 82K values.