In the United States we have all across this country, we have dozens of Halakha courts, in which particularly observant Jews can take these issues of family law to an orthodox Court and have that judge, judge for them. As long as the courts don't violate the laws of the land and as long as there's a room for appeal should one or two parties disagree with the verdict, I don't see how this would have anything to do with being incompatible with what we refer to as Western ideas of democracy.