One of the major problems in most societies, subject to "great sorts" of various kinds, is the fact that people observe correlations of attitudes & beliefs, and infer from those necessary relations. For example, if one of the first things that someone finds out about me is that I am an atheist, there is a general presupposition that I am a Left-Liberal. It is true that there is a robust relationship between atheism and liberalism in the United States, the problem I have, as an admittedly illiberal atheist, are those who believe that atheism entails liberalism. In a specific instance I have encountered secular proponents of abortion rights and gay marriage who simply find it hard to conceive that someone would have reasoned objections to these policy positions which were not fundamentally rooted in religion. A cursory examination of the treatment of homosexuals in Cuban or the old East Germany would show religion is not necessary for intolerance of homosexual behavior. But instead of focusing on such details of history, I think it is important to note there are societies which are both far more secular than the United States, and more socially conservative: those of East Asia. Instead of asserting this, let's look at the World Values Survey. I use both the WVS 2005-2008 & Four-wave Aggregate of the Values Studies, explaining the duplicates for nations in the tables below. Additionally, I would caution some care in overemphasizing any specific row because of some small sample sizes, in particular the number of convinced American atheists in the Four-wave Aggregate of the Values Studies (n = 17). Below are attitudes to a host of social and political issues in several East Asian countries and the United States. I also later broke these out by religious criteria.
Family Very ImportantReligion Very ImportantActive Member of ReligionAbortion Never Justifiable
Homosexuality Never JustifiableWould Give Money For Environment – Strong AgreeNever Justifiable For Man To Beat WifeReligious Person – Yes
Believe in God -YesGod Very Important In LifeProstitution Never JustifiableEuthanasia Never Justifiable
Divorce Never JustifiableScientific Advances Will HarmIncome Differences Necessary IncentivesCompetition Is Good
Economic Growth Increase Everyone's Wealth
Hard Work Brings Better Life
Abortion Never Justifiable
Homosexuality Never Justifiable
Euthanasia Never Justifiable
Prostitution Never Justifiable
Competition is Good
Men Have More Right To A Job Than Women
Men Make Better Political Leaders
Incomes Should Be Made More Equal
Economic Growth Increase Everyone's Wealth
I think you can see several general trends: 1) The United States is the most religious of these nations 2) It is arguably the most Left-Liberal as well 3) There is definitely some trend toward Left-Liberalism being associated with irreligiosity in East Asian nations, but far less so than in the United States Let's just compare the proportions for atheists vs. those who are religious in each row and sort them by value. By this, I mean that if the proportion for a particular question for the religious = 40%, and atheists = 40%, then the ratio = 1. On the other hand, if the religious = 40% and atheists = 10%, the ratio is 0.25. So a value around 1 indicates little difference between those who are religious and those who are convinced atheists, while a value deviated far from 1 indicates great differences between the two sets.
I bolded China and emphasized the United States because I think it is clear from these data that the USA and China manifest two different tendencies. In the United States the religious and atheists have very different socio-political profiles. The stereotypes that American religious social conservatives hold about atheists are justified, and those that liberal secular individuals hold about religious people have some foundation. On the other hand in China there is minimal difference between those who see themselves as religious and those are atheists; in fact, if you look at the data I'm not so sure that the atheists aren't exactly somewhat more conservative, at least in the Milton Friedman libertarian style (I think this has to do with correlations of age, sex and education, but I won't get into these data). In any case, I think there's a simple explanation for the difference between the USA & China when it comes to atheist vs. religious attitudes. Again, from the World Values Survey:
Notice something? Atheists in the United States are an extremely small fraction any way you slice it. As such, they are probably selection biased toward particular segments & personalities who would be willing to risk nonconformity. In contrast atheists are a much larger proportion of the population in China, where they are approximately equal in numbers to the religious, and both groups are outnumbered by those who are not religious, but would not assert an atheist self-identification. My point here is rather simple: increased secularism in the United States would almost certainly lead toward a shift to greater Left-Liberalism. But that dynamic will almost certainly exhibit diminishing returns as secularization proceeds and the personality and social profiles of atheists starts to converge upon the general population. The bad news for conservatives is that I think the secularizing tendency in America during the current period is good for liberalism. The good news is that it probably isn't as bad as it could be if you extrapolated on a straight line from the current secular population in terms of political outlook.