Summary: it is a prerequisite that you think you are entitled to your own beliefs, your beliefs matter, you think your actions follow your own beliefs and not from commands issued by others, and your actions can make a difference, at the very least in your own life. This may correlate with what one may call either equality or liberty.
Religion as not even attire, just obedience
I know people, mainly old rural folks from CEE, who do not think they are entitled to have a vote in whether there is a God or not. They simply obey. This does NOT mean they base their beliefs on Authority: rather they think their beliefs do not matter, because nobody asks them about their beliefs. They base their behavior on Authority, because this is what is expected of them. The Big Man in suit tells you to pay taxes, you do. The Big Man in white lab coat tells you to take this medicine, you do. The Big Man in priestly robes tells you to kneel and cross yourself, you do. They think forming their own beliefs is above their "pay grade". One old guy, when asked any question outside this expertise, used to tell me "The Paternoster is the priests's business." Meaning: I am not entitled to form any beliefs regarding these matters, I lack the expertise, and lack the power. I think what we have here is not admirable epistemic humility, rather a heavy case of disempoweredness, inequality, oppression, lack of equality or liberty and of course all that internalized.
Empoweredness, liberty, equality
Sure, on very high levels liberty and equality may be enemies: equality beyond a certain level can only be enforced by reducing liberties, and liberty leads to inequality. But only beyond a certain level: low and mid-levels they go hand in hand. My impression is that Americans who fight online for one and against the other simple take the level where they go hand in hand for granted, having had this for generations. But it is fairly obvious that on lower levels, some amount of liberty presumes some about of equality and vice versa. Equality also means an equality of power, and with that it is hard to tyrannize over others and reduce their liberties. You can only succesfully make others un-free if you wield much higher power than theirs and then equality goes out the window. The other way around: liberty means the rich person cannot simply decide to bulldoze the poor persons mud hut and build a golf range, he must make an offer to buy it and the other can refuse that offer: they negotiate as equals. Liberty presumes a certain equality of respect and consideration, or else it would be really straightforward to force the little to serve the big, the small person goals and autonomy and property being seen as less important (inequal to) the grand designs and majestic causes of the big people.
The basic minimal level where equality and liberty goes hand in hand is called being empowered. It means each person has a smaller or bigger sphere (life, limb, property) what his or her decisions and choices shape. And in that sphere, his or her decisions matter. And thus in that sphere, his or her beliefs matter and they are empowered to and entitled to make them. And that is what creates the opportunity for rationality.
Harking back to the previous point, your personal beliefs of theism or atheism matter only if it is difficult to force you to go through the motions anyway. Even if it is just an attire, there is a difference between donning that voluntarily or being forced to. If you can be forced to do so, plain simply the Higher Ups are not interested in what you profess and believe. And your parents probably not try to convince you that certain beliefs are true, rather they will just raise you to be obedient. Neither a blind believer nor a questioning skeptic be: just obey, go through the Socially Approved Motions. You can see how rationality seems kind of not very useful at that point.
Silicon Valley Rationalists
Paul Graham: "Materially and socially, technology seems to be decreasing the gap between the rich and the poor, not increasing it. If Lenin walked around the offices of a company like Yahoo or Intel or Cisco, he'd think communism had won. Everyone would be wearing the same clothes, have the same kind of office (or rather, cubicle) with the same furnishings, and address one another by their first names instead of by honorifics. Everything would seem exactly as he'd predicted, until he looked at their bank accounts. Oops."
I think the Bay Area may already have had this fairly high level of liberty-cum-equality, empoweredness, maybe it is fairly easy to see how programmers as employees are more likely to think freely about innovating in a non-authoritarian workplace athmosphere where both they are not limited much (liberty) and not made to feel they are small and the business owner is big (equality). This may be part of the reason why Rationalism emerged there (being a magnet for smart people is obviously another big reason).
Having said all that, I would be reluctant to engage in a project of pushing liberal values on the world in order to prepare the soil for sowing Rationalism. The primary reason is that those values all too often get hijacked - liberalism as an attire. Consider Boris Yeltsin, the soi-disant "liberal" Russian leader who made the office of the president all-powerful and the Duma weak simply because his opponents at there, i.e. a "liberal" who opposed parliamentarism (arguably one of the most important liberal principles), and who assaulted his opponents with tanks. His "liberalism" was largely about selling everything to Western capitalists and making Russia weak, which explains why Putin is popular - many Russian patriots see Yeltsin as something close to a traitor. Similar "sell everything to Westerners" attitudes meant the demise of Hungarian liberals, the Alliance of Free Democrats party, who were basically a George Soros Party. The point here is not to pass a judgement on Yeltsin or those guys, but to point out how this kind of "exported liberalism" gets hijacked and both fails to implement its core values and sooner or later falls out of favor. You cannot cook from recipe books only.
What else then? Well, I don't have a solution. But my basic hunch would be to not import Western values into cultures, but more like try to tap into the egalitarian or libertarian elements of their own culture. As I demonstrated above, if you start from sufficiently low levels of both, it does not matter which angle you start from. A society too mired in "Wild West Capitalism" may start from the equality angle, saying that the working poor do not intrinsically worth less than the rich, do not deserve to be mere means used for other people's goals but each person deserves a basic respect and consideration that includes their beliefs and choices should matter, and those beliefs and choices ought to be rational. A society stuck in a rigid dictatorship may start from the liberty angle, that people deserve more freedom to choose about their lives, and again, those choices and the beliefs that drive them better be rational.