In recent times in Australia, there has been debate about this matter, following criticism of the Victorian government's recent reconsideration of religious bodies' total exemption from the Equal Opportunity Act. The problem in a nutshell is that democracy provides no guarantee of Christian values even in a Christian country.
Cardinal George Pell, the Catholic Archbishop of Sydney has in the past argued the Democracy must change to counter Islam, noting that "democracy was not a good in itself. Its value depended on the moral vision it served."
Only last week, former Prime Minister John Howard argued against a Bill of Rights - something almost every other democracy has - on the basis that democracy itself (ie the legislature) is the best safeguard for rights and not unelected "elitism" (ie the judiciary). This argument goes back to the founders, and is indeed the reason why no Bill of Rights was included in the first place.