If you own more than one set would it be possible to pair both to the same device at the same time so that two or more people can listen to the same music? If so would it matter if the sets got mixed up?
This isn't possible but on Mac you can use AirPlay so that one application outputs audio to one audio device and an other application outputs to an other device.
On Mac it might be possible to listen to the same audio stream on more than one audio device, but I don't know what or how many applications you need to use to achieve that. Basic idea is that you need to send the audio to a special software audio device that splits and sends the audio to two or more hardware audio devices.
You can have multiple sets of AirPods paired to your devices and switch between them without issue - indeed I've done this for a while now without issue - but you can't output audio two sets of AirPods from the same iOS device at the same time, as OP wanted.