Valid concern. First we need to dispose of the idea that Islam is a religion...unless they’re willing/able to decouple politics (i.e., bombings) from it.
If the KKK had bombed the World Trade Center, I doubt President Bush would have been posing with one of their Grand Wizards and saying that the WTC bombers do not represent true Klan-ship, but rather were people claiming to be KKK, trying to make the Klan look bad.
The average American does not understand how Islam is also a political and legal system. Most have no idea what things like the caliphate, sharia, jizya, dhimmi, etc. mean. It’s going to be a tough job getting people not to associate Islam with religion. I just don’t know if it’s really possible, because of course there is a religious element to it too.
I foresee a possible time in the future, for example, when a left-wing government wants Fundamentalist Christians and Orthodox Jews monitored and tracked, because of their supposed “hate speech” (anti-gay marriage, etc.) and “intolerant” views. I don’t want them to be able to claim there is a precedent for this.