JimmyD, thank you for your opinion!
I contacted the organization directly and received a reply from their secretary and editor, Per-Olof Svensson. He confirmed that the badge has no connection with Blå Bandet. He also pointed out that the organization historically used the abbreviation SBF, not SBB, and that a skull-and-crossbones would never have been used in their symbolism.
So that lead can now be ruled out. The mystery continues, and I'm still looking for any information about this badge. Any new ideas would be greatly appreciated.