The problem with allowing people to submit to some kind of religious law, as an act of their own religious freedom, is when that submission sometimes comes into conflict with the law regarding certain acts prescribed for those who violate the religious law. The Mormons, for example, have a principle related to their doctrine of blood atonement, stemming from their belief that the blood of Christ is not sufficient to atone for all sin, partucularly the sin of murder, and that the sinner must atone with his own blood. It wouldn't be a good idea to allow the church to exercise this rule of religious law, and so the church officially outlawed its practice, as it did with polygamy, though there are renegade groups which continue to practice both.
Sharia law invokes the death penalty for a number of offenses, or advocates punishments which would be considered cruel and unusual, and which would not involve any violation of civil law. It wouldn't be possible for someone to submit to it and not have their civil rights violated.
I think a lot of what we are seeing now involves some kind of hysteria spread in the wake of 9-11, and of all the rumor mongering and lying that has gone on about President Obama's supposedly being a closet Muslim. That's the sort of thing that demonstrates an appalling ignorance of the constitution, of the general functioning of the US government, and of world events in general, not to mention a mountain of evidence which indicates otherwise. It's just more tea party extremism.