Why wouldn't there be a database of Muslims? It's so rational for any powerful group to have a massive database. It's just that instead of having a DB of Muslims, you'd have a DB of citizens, of which Islam would be one of many fields. Perhaps this is what you meant by the FBI database.

Also, having a database of many kinds of information is rational because it doesn't have the same fear factor as a database of Jews, and yet it has that same power -- if the political winds should ever blow in that direction.