Are BMX threaded headsets and other threaded headsets interchangeable?
No, they're not interchangeable. BMX 1" threaded headsets have an outer cup diameter of 32.7mm - they wouldn't fit in a standard road frame. Standard (ISO) threaded headsets have an outer cup diameter of 30.2mm - they'd fit loosely in a BMX frame.

Sheldon Brown's Bicycle Headset Dimension Cribsheet is a useful reference for headset interchangeability.