It is a totalitarian political movement that has co-opted religion into its movement, and adopted criminal practices. Those political and criminal elements must not receive the protections of religion. Religion is protected to protect the individual’s freedom of conscience, not to shield criminal behavior from enforcement.
Your point is strongly made. Except, being realistic, the USA is never going to modify the First Amendment to exclude the practice of what is considered one of the world's "great religions". We're never going to say to the millions of Muslims who are law-abidi9ng citizens of the United States that they can't continue to practice their religion.
As you note, there are statutory exceptions made to free speech. But the exceptions to freedom of religion that I'm aware of are all exceptions to statutory law -- native American religions are allowed to use peyote, etc. Hell, we even allow the practice of Satanism (so long as it doesn't involve the sacrifice of humans).
Accordingly, we've got to find another way to isolate and control the Islamic terrorists. "Sharia law" offers an opportunity to do so. While it's bound up as part of the religion, it is, in fact, a set of laws that control everyday life, a system of governance.
Thus, Sharia Law could be banned -- just as we, at one time, banned Communism (and probably should again). Sharia Law is clearly incompatible with the Constitution and any practicing Muslim (or Mullah) who insisted on following Sharia Law could be declared persona non grata or barred from entering the country.
We're never going to outlaw Islam. But we could conceivably outlaw Sharia Law.
There is no need to modify the first amendment to prosecute, spy on, or censor Islamists.
Just as people are prosecuted for slander, libel or sedition despite the first amendment’s grant of free speech The constitution must be interpreted to apply to specific cases. The wording of amendments is not absolute, especially when it conflicts with other rights and laws.
Sharia law is inherent in Islam - it is based on the same claim of absolute, unchallengeable authority which is the basis of Islam - Shahada, the first pillar of Islam, which jihadis invoke every time they throw their gang sign of the right pointer finger pointing upward - There is no God but Allah, and (only) Muhammad is his prophet. Divine authority trumps all.
The most central and pernicious elements of Islam are in the Koran and the Hadith (the stories/example of the life of the prophet), upon which Sharia is based. You can do away the implementation of Sharia, and it would still allow the preaching of genocide, dictatorship, slavery, pedophilia, murder, rape, etc.
Yes, we would be fools to allow Sharia to be accepted as legitimate - but that alone is inadequate to counter subversion. The protection of a claim of religious immunity must be removed from those who advocate violence, Islamic supremacy, or hatred. Laws already exist to prosecute such offenses - they must be prosecuted even if defendants can clearly show that this is straight from the Quran, and is legitimately part of Islamic doctrine.