Mutually exclusive
Irreconcilable differences
Incompatible
Polar opposites
The following terms come to mind:
Military intelligence.
Just as Communism was actually projection of Russian (and Chinese) power, so modern Islam is actually a projection of Saudi (and Iranian) power. Making this a First Amendment question is just as misguided as thinking the Cold War had anything to do with economics. The stated goals are a distraction from enemy action.
It would be best not to nuke Mecca or Medina, but use MOABs on the palaces of Riyadh and Tehran. Stop the flow of money to madrassas and terror cells worldwide, stop the threat from Islam.