On the question raised by Ben Carson, the correct answer remains that given by Colin Powell (a Republican, it should be pointed out) or the one given by a Founding Father (that I am still looking for an exact reference for; basically that if the people elected even a "Mahomedan", it should be fine by us).
On the wider issue, the way I see it, the issue isn't Islam or Muslims (whatever your local CAIR rep might say), but bigotry generally. My problem is that way too many Muslims--even those who might look like they don't make their faith an issue--agree with Dr. Carson that Islam and the US Constitution don't go together. Just as there are Christians, Hindus, and others that want no part of "Man Made laws". While they can hold what opinion they want, I--and you can look at my About page on Facebook--was brought up to be a "Constitutional Muslim", one who believes that living under written laws is not just acceptable, but the ONLY way to go for a Muslim in this day and age. (See also this previous post.)
After all, The Prophet actually headed a multi-ethnic, multi-faith confederation for the last part of his life--one that was governed by a written constitution that provided for each sub-community and faith community to be governed by its own laws. (See https://en.wikipedia.org/wiki/Constitution_of_Medina)
And lastly, why are we giving a troll like Ben Carson—who is never going to be more than a flash in the pan—so much mindshare? I do appreciate that his actions give us the chance to have this conversation. And that he and Donald Trump are basically forcing the reboot of the Republican Party that this country needs, to keep the political system healthy. But if we could have these conversations without privileging bigots like that, the world would be such a better place.