Whirling Dervishes

The Mevlevi have always been ecumenical in outlook, welcoming non-Muslims to the sema in the belief that all people are equal in the sight of God. (Seljuk society was an equally ecumenical place: a ruling class of Turks and a populace of Byzantine Greeks, Jews, Armenians, Kurds and others).
Rumî's most famous writing is his invitation to the sema:

Whoever you may be, come
Even though you may be
An infidel, a pagan, or a fire-worshipper, come
Our brotherhood is not one of despair
Though you have broken
Your vows of repentance a hundred times, come