While the traditionally Christian nations have "lost their faith" please do not believe that governments have stopped pushing Christianity. Most of sub-Saharan Africa is governed by Christianity and it is held higher than government or tradition. Other nations like the Philippines or Armenia are also comparably Christian to a high medieval era European monarchy. Support has waned in some areas, and others, like South America, it is the unwritten law.
These myriad nations are not particularly less than those under direct control by Islamic elements. (Although true direct control be religious leaders only brings Iran to mind.)
I agree with your idea that rule by ideology, whether religion or the psuedo-science (or nonsense) supporting nationalism, is very dangerous. I don't think governments appreciate this kind of epiphany, however, because it relegates them to being merely servants of the people, and politicians like to think that what they do is really awesome and that they should be able to tell people what to do because they are just powerful people.
I grant you sub-saharan africa. The nations with history connected to Europe have no more official authority on how Christianity should be followed or scripture interpreted. This is tied to the history around the 30-year war that broke up the idea of a religious authority. The catholics still have a religious authority but only if you choose to be a part of that religion. They have no official power to enforce any law.
The protestant monarchies fell one by one and were converted to democracies. After World War II the state-churches had to give up their authority in favor of religious freedom. Ironically this meant the reestablishment of the catholic church in many of the now "protestant" countries as well as "acceptance" of Judaism and now various islamic groups. We are in an era now when even the deeply religious understand that without secularism their freedom to practice their religion is bye bye.
The American south is a different affair. It's not that they have government support to enforce religious rule, it's just that the people interpreting the laws and the people who elect them tend to be highly religious, but even in the deep south you will get objections if you quote bible passages that doesn't fit peoples taste. Also you have phenomenons like the Mega Churches that ride on capitalism to carve out new domains of power. Unfortuntely you have a strong history-revisionist movements and a broken school system so the legal system is undoing itself simply thanks to people disbelieving it's existence.
That said, the replacement for religious authorities is this fleeting identity where "true christian" have as much coherence as "true american". People load it's content with their own subjective opinions, very few read scripture and even those who do are called things like "bible-thumpers" or "zealots" by the "mainstream christianity".
In comparison there
are "muslim strongholds", official government-like authority structures who claim to stand for "Islam", but just like the Catholic Church they are just authority-structures with human beings enforcing their own opinions. Like Christianity, these strongholds disagree, they are strongly tied to nationalism and local traditions and there are many dissidents who, based on different Islamic interpretions, question their rule.
But under what banner should the people unite?
My suggestion; humanity. I have given it some thought during the past years after studying how group-identity works. I believe that it is possible to see "humanity" as your group, considering those who support "humanity" as friends and those who attack "humanity" as your enemies. Of course, I am not the only one who came up with that idea, the following animation explains the idea well, including some of it's scientific foundation;
http://www.youtube.com/watch?v=l7AWnfFRc7g
The important part I believe is that I do not say "human", I refer to no single human being. The reason is that as long as a person try to work for humanity (or humankind) they have no affiliation to minor subgroups, their affiliation is to the inclusive ideologies of the world, those who wish to connect, grow and build, rather than divide and reject. By accepting humanity as your group you actually gain most of the cognitive benefits of belonging to a group, but skip many of the sideeffects. You can even solve the "without god" issue and you do believe something larger than any local government.
And yeah…