A lot of Islamic scholars got together to list all the stuff ISIS does wrong: http://www.lettertobaghdadi.com/
If you don't want to visit the site, here's the summary:
>Islam forbids the issuing of fatwas without all the necessary learning requirements. One must consider the entire Qur’an and Hadith, when delivering them;
>It is forbidden in Islam to issue legal rulings about anything without mastery of the Arabic language
>It is forbidden in Islam to oversimplify Shari’ah matters and ignore established Islamic sciences.
>It is permissible in Islam [for scholars] to differ on any matter, except those fundamentals of religion that all Muslims must know.
>It is forbidden in Islam to ignore the reality of contemporary times when deriving legal rulings.
>Islam forbids killing of the innocent, emissaries, ambassadors, and diplomats; hence it is forbidden to kill journalists and aid workers.
>Jihad in Islam is defensive war. It is not permissible without the right cause, the right purpose and without the right rules of conduct.
>It is forbidden in Islam to declare people non-Muslim unless he (or she) openly declares disbelief.
>It is forbidden in Islam to harm or mistreat—in any way—Christians or any ‘People of the Scripture’.
>It is obligatory to consider Yazidis as People of the Book.
>The re-introduction of slavery is forbidden in Islam. It was abolished by universal consensus.
>It is forbidden in Islam to force people to convert
>Islam forbids to deny women and children their rights.
>Enacting legal punishments without following the correct procedures that ensure justice and mercy.
>It is haraam to mutilate the dead and to torture people.
>It is forbidden in Islam to attribute evil acts to Allah.
>Armed insurrection (baghy) is forbidden in Islam for any reason other than clear disbelief by the ruler and not allowing people to pray.
>It is forbidden in Islam to declare a caliphate without consensus from all Muslims.
>Loyalty to one’s country is permissible;
>After the death of the Prophet, Islam does not require anyone to emigrate anywhere.
Funnily enough one of the big guys who supports ISIS doubled down and claimed that everyone who signed the list wasn't a real Muslim.