Christianized public morality. There's a theory that goes that the schemes of non-religion based morality developed during the Enlightenment period really just enshrine Christian values in abstract philosophical forms, and that these forms don't necessarily lend themselves only to the interpretation that the Philosophes gave them. If that's so, then the sort of secularized philosophy that we're trying to sell other countries on may be Christianity in another form, with secularized versions of Islamic morality, Hindu morality, Buddhist morality, possible as well. But how do you prove it? There's an interesting and popular philosopher many people have heard of who called society's bluff on the subject: Friedrich Nietzsche.
Yes, good old Nietzsche. Nietzsche is regarded as an extremists, as a misanthrope, as an advocate of values that really shouldn't be put into action, and he's no doubt guilty of some of these, but the question is why, after living in an environment where secular morality based on empirical evidence supposedly rules the day, does he offend people? I mean if there is no god and Christianity is a swindle, then why is Nietzsche's worldview, praising war and warlike virtues, stamping out compassion, explicitly acting Machiavellian, regarded as wrong? Surely you could come up with arguments based on observation that prove that hostile, pagan, values can lead to some sort of public morality and social system---not purely to complete chaos and destruction?
If this life in front of us is all there is then why not Nietzsche? I think the answer is that despite claims of being Enlightened and above superstition people have just enshrined Christian values in new forms. I'm not saying that I'd like to live in a society where Nietzschean morality ruled the day, but such a thing shouldn't, in theory, be abhorrent to people who are truly atheistic in their morality and in their conception of public life.
For that matter, getting even more cynical, why not de Sade and Sadean morality? After trashing Sade in relation to another Libertine writer I went back and started reading "Justine" to be sure that I hadn't misrepresented Sade. If there's no god, which Sade reiterates time and time again as his thought on the subject, then why not engage in Sadean exploitation against people, using them as playthings and throwing them away when the whims of the physically stronger have been satisfied?
This brings up quite a lot of questions, the biggest one being where should morality go if it's not constrained by traditional religious beliefs? There are answers to that, it isn't just some sort of taunting argument that a preacher would give to a kid asking why he or she should care about what the bible says.
But in exporting our secularized morality to the world, and getting upset about practices and moral standards that we don't consider to be properly "enlightened" and rational, the west often commits the sin of cultural imperialism. We object to them first because of our own Christian biases, and then standing behind the Christianity is power---state power, economic interests, corporate power---all delighting in using Christian standards, whether secularized or not, to justify exploiting another culture, another country, for their own benefit.