Iran is the birthplace of many branches of Sufism. My father was once interested in them and went so far as visiting some of their places and even showing us their photos books etc.
  They are known for their odd behaviors (eg. stabbing themselves without bleeding, knowing "secrets" etc.). Their beliefs include:

1-contempt for natural and human joys.
2-contempt for human logic and human philosophy, emphasis on holy craze.

3-emphasis on "esgh" or "asq" which is translated love but is very different from agape, erose and other things we have in our faith. It is an unconditional, unknowable, shapeless, nameless union with god without any regard for eternity. free will and goodness has no place here. You must be chosen before birth.

4-idea of pre-existance of soul.

5-dances and swoons and wonderworks.

  And to our surprise: the idea of having holy spirit in them! The name of the holy spirit is in quran though not as God, but as an angle. Even the famous persian poet "Hafiz" names him as a 'spiritual, impersonal source of power'.

  Now my question: don't they remind you of several heresies like charismatics for example?

If I remember right, John Vennari did research on the Charismatic movement here in our country. And, your point is that Sufism and the Pentecostal Charismatic movement that has been swallowed hook line and sinker by novus ordos here mirror each other. I do not know much on this subject, however you are right in the things they do (my father was from the south and a family of Petecostals. Had poisonous snakes they would subject people to for one). And, then my mother used to run with them here in Illinois and there was much strangness involved. People barking and so on. She said they did the crazy dances and called 'The Spirit" down on themselves. Course when it makes people roll on the floor and bark like a dog right there is a clue it is not God. And, also, there was always some priest their from Medjugore  (sp?) that supposedly had the stigmata so there is the religious mystic as in sufism. Am I  wrong please correct me dear Spouse.

Now, Dear,  you know why they are the same. Prots and Muslims both have the Prince of This World as their head. They do not accept Jesus Christ or they would be Catholic. Satan has been whispering his nonsense in ears since Adam and Eve.