Setting audio output impedance for output protection

Which circuit you want depends on specifications you haven't told us. The important question is what exactly is supposed to happen when a user connects the outputs of two of these things together?

If they really aren't intended to be connected together, then the resistor is just for protection. In that case, your second circuit is better. You set the resistor value to not exceed the opamp's output current capability under the worst case conditions.

If multiple modules are intended to be tied together and you're supposed to get the average result, then you need to use your first circuit. This would be the case, for example, if it's allowed within the specs to connect the left and right channels together to get mono. In that case, the resistor needs to be whatever the specified output impedance of each module is supposed to be. If they are supposed to average by shorting, then each needs to have a defined and controlled impedance. That impedance must be specified by the standard.

For example, if you were to pick 1 kΩ and someone else picked 10 kΩ, then connecting the two modules wouldn't yield the average as intended. The resulting signal would be 10/11 parts from your module and 1/11 parts from the other module. For the averaging scheme to work, all the impedances need to be equal, and therefore agreed upon ahead of time.

The two circuits respond differently to an external load to GND. Using an extreme case to demonstrate, assume a 1 K resistor to GND as the load. In the first circuit, the opamp output pin voltage does not change, the circuit gain does not change, but the external voltage decreases 50%.

In the second circuit, you now have a 50% attenuator inside the feedback loop. Before, the right end of R2 (68K) was connected to a zero ohm voltage source. Now it is connected to a Thevenin equivalent voltage that is 1/2 the opamp output voltage, through a equivalent 500 ohm resistor.

So the feedback resistor value is different, which changes the circuit gain, and the feedback voltage is very different, which really changes the gain. The opamp output pin voltage will double (approximately) as it tries to close the loop. The external output voltage will not decrease much until the opamp saturates. Or something like that.