Muharram processions are specific to the Shia community. Allowing one and not letting Sunnis or Sufis do some arcane street ritual/procession is recipe for disaster. Best to not allow anything. Let these rituals be relegated to the mosques and Imambaras, not on the streets where they hamper with the daily lives of non-Muslims.

Indigenous Muslims that you had mentioned are my absolute favorite kind of people, that I've eschewed the rest. The rest could actually learn a thing or two from them (but of course they won't).