I’ve searched through the internet and found only a couple of threads regarding this problem, but none were really marked as a “bug” and no one knew the reason. I think I know what is happening and I even found a workaround, without needing to start the whole mission anew.
I bugged out the 4th band member on the bench near the stage, when I talked to Martinez right in front of him as the Shaman. He woke up because of that, but not the way the game wanted it. This way he ends up just standing there, watching me walking around, not reacting, not doing anything, never arriving at a stage.
You can’t trigger his “I’ll see if they are still on the stage”, because he is bugged out and you cannot talk to him, like you usually would be able to.
Throw something (e.g. a soda can) near him. Then go around the house he is at, back to him. The conversation starts, as if you have started talking to him. Now the band story mission works again.