I’ve a fair few Muslim friends (Ramadan Mubarak to any Muslim Dopers reading) and they’re adamant that Islam had no equivalent of a Pope, or Tsar, or Emperor - any human who can claim a greater connection to God than anyone else. In other words, a Muslim is accountable only to God and him/herself.
They’re also pretty clear that Islam is supposed to be unchanging, that adding, retracting or amending the Quran would be an act of blasphemy as Mohammed had the final revelation.
So…how does a religion meant from day 1 to be as orthodox and unchanging as possible have such different views on authorities (secular or spiritual)? Where do ISIS get the idea that they have authority over all Muslims - is there anything in the Quran about people in authority (like the Bible’s “render unto Caesar”)?
Neither does Judaism. We did have the Kohen. But we haven’t had one of those for quite a long time now.
If I’m wrong one the SDMB’s industrial strength Jews will correct me. But, this is mostly true of Judaism as well. You can add whatever commentary you want to the talmud, but the original words of the torah cannot be changed in any way. Judaism also holds that there are no more prophets. This was a big reason why Jewish leaders of the time didn’t accept Mohammed (PBUH) as a prophet.
A more knowledgeable Doper will inform you on the Caliphate, the split between Sunni and Shia and so on.
As for where Isis gets the idea that they have authority over all Muslims, I dunno.
ETA
Re Render Unto Caesar
In Cows, Pigs, War And Witches- The Riddles Of Culture, Marvin Harris asserts that Jesus was here alluding to an earlier speech (just as anybody who says “I have a dream” is referencing Dr King) in which the speaker (my copy of the book is on loan to a friend and I can’t recall the speaker’s name) said that EVERYTHING in the Holy Land belonged to G-d. By this logic Jesus was saying, in a way that the Jewish crowd would understand and the Romans would not, give nothing to Caesar. Everything here is the Lord’s
Judaism still has Kohanim. They just don’t really do very much anymore.
But to answer the OP, the Caliph is the Caliph to the extent that he’s recognized as Caliph by the Muslim community. That group can call their leader Caliph, but he’s not recognized as it by anybody outside their group. In theory, the Caliph is the successor to Mohammed, and the leader of all Muslims. In theory.
Where does the leader get the idea that all Muslims must follow him? Likely the same place bin-Laden got the idea that he had authority to issue fatwa: pulled it out of his tush.
The Caliphate is certainly an office that is well-grounded in Islamic history, and theoretically speaking a Caliph does have the right to demand an oath of allegiance from Muslims everywhere. Unfortunately for ISIS, I do not see how they have given any reason for any Muslim outside of their violent reach to accept Abu Bakr al Baghdadi (who they are now calling by his real name, Ibrahim) as Caliph.
The Qur’an is a short book that does not contain specific instructions on most things, and is often unclear. This, unsurprisingly, led to differences in opinion on how to handle real-life issues. These differences of opinion were exacerbated over time, first by the sheer width and breadth of Muslim communities, and more recently by the modern de-legitimizing of traditional structures of religious authority.
As the others say, the only basis for this claim by this group is their own assertion. The basis of the idea of the Khalifa is not actually clear in the Quran, it is the Hadith and Sunna more than the Quran.
But since the fall of the Ommayid of Baghdad, there has not been one single Khalifa, but competing ones.