I've never been entirely sure about that. Even reading about it now, it's not completely clear. The Wikipedia page gives some clues when it says "a major theme of that novel is the dangerous nature of closed, absolutist belief systems" and when it refers to "the satiric nature of the work".
https://en.m.wikipedia.org/wiki/The_Satanic_Verses
It would seem to me to be the reference to The Satanic Verses is what got Rushdie in such trouble.
Like Judaism, Islam is based in earlier religions that were largely polytheistic and retains some elements of it. The Satanic Verses are a revelation to Prophet Muhammed that mentions three goddesses, the Cranes, who are actually two (two names in the scripture belong to the same goddess), later Muhammed rejected the revelation because -mentioning the goddesses- it must have come from Satan.
Jesus had a Satanic revelation. It happens all the time in religion!
There's a documentary about Petra in Jordan, being the actual city where Muhammad was in The Quran on youtube, rather than Mecca. It also goes into detail about the likely pre-Islamic sources of Islam, among other things the Egyptian and Greco-Roman influences (one of the Cranes is linked to Demeter).
In The Satanic Verses the existences of the goddesses was acknowledged, but later Muhammed himself rejected them on account of it not fitting in Monotheism, and therefore. it became forbidden.
And those that cross whatever bounds Allah has supposedly laid down -however trivial- are murdered.
I suggest we call out religious denominations for the violence they do in the name of religion.
I suggest we call out our politicians for their appeasement of these groups who support these murders and their attempts to keep order by silencing their critics.
In Western society, there's a difference between wanting to kill someone, which is normal, and actually going out to murder them. It would be well for far too many Muslims to learn this.