Obviously I'm in the camp that considers declining birth rates to be a serious problem for the liberal West, and so obviously I agree with Megan's point that "the most important core beliefs most people have are transmitted not through dialogue, but through inheritance," and its corollary that no matter how "immense" and "salient" the rewards of the "liberal market culture" that Will favors, it will be much harder to pass it on down through conversion than through child-rearing.
The most important core beliefs most people have are transmitted not through dialogue, but through inheritance. It is extremely likely that you share the political views of your parents, their religious affiliation, and at a less obvious level, their beliefs about things like what constitutes stealing and lawbreaking, and what are justified evasions of petty laws.
I'm enough of a cultural relativist to believe that other cultures have a perfect right not to adopt American values, but enough of a cultural hegemonist to know that I want my country to maintain the dominant American culture.
I'm not enough of a cultural hegemonist to care whether the people living on this particular piece of land maintain the dominant American culture into perpetuity; if, in the year 3000, the entire world is dominated by Danish mores, I will not feel slighted. Still, the "conversion versus inheritance" debate is a relatively unhelpful way to approach the issue. The word conversion suggests a wholesale repudiation of one set of beliefs and acceptance of another, but cultures shift as the result of millions of choices at the margin. Europe is rapidly secularizing; you wouldn't call that inheritance, nor would you call it conversion. (You might call it spiritual drift, though I tend to think they're drifting toward something better.) The conversion/inheritance framework assumes that the host culture remains static as outsiders bend to its dictates; it allows for no single person to claim a place in more than one tradition; and it fails to acknowledge that we are moving toward a more mobile society with ever more return and circular migration. As William Marling has pointed out, much of what is derided as "Americanization" is really just modernization. It does represent a kind of convergence, though not much of a takeover.
I have more faith than Megan does in rapid assimilation toward liberal norms among individuals who have self-selected to come and live in the United States, but we agree that assimilation is possible and desirable. On the other hand, fertility alarmists tend to make very odd assumptions about the way people engage with a dominant culture over time. If you assume that today's day laborers are static representations of a single unchanging culture frozen in the year 2008, and will go on to produce tiny Mexican-flag-waving mariachi babies in the year 2020, you may well be worried that 30 percent of the U.S. population will be Latino by 2050. If you don't, it might occur to you that most of that 30 percent will be indistinguishable from the general population by 2050, not just because they have changed dramatically but because you have slightly.
Part of the reason we find it so difficult to think about demographic change is that we fail to notice the goalposts changing around us. It's true that the people we call social conservatives in this country are reproducing faster than the people we call social liberals. But what will it mean to be "conservative" in America a century from now? In 1908 being a social conservative meant something far less amenable to tolerance than "legal marriage is for straight people!" Yes, Utah's birthrate is higher than that of Bangladesh. I don't know how to worry about that particular factoid, because I have no idea what it will mean to be a socially conservative Mormon in 30 years. It certainly means something different today than it did 30 years back.