I think the problem of hyper-religious subgroups out-reproducing the rest of society is a problem that will eventually come for all First World societies, and Israel is simply ahead of the curve of the rest of us.
I don't see it. What groups in Christendom are really like the Haredim? The obvious examples are the Mennonites and Jehovah's Witnesses. Maybe you can make a case for Calvinists in the Netherlands, but I don't know to what extent they segregate themselves from broader society. There are pietistic Lutherans in Finland but they are a very small group. Presumably there are other groups in other countries that I can't name, but I am comfortable in saying that none of them are significant. Evangelicals in Brazil and elsewhere don't count because they are part of broader society. The same is true of Mormons. I know you said the First World specifically, but I will also add here that I'm not aware of any groups like this in the Islamic world.
It seems self-evident that religious people are more fertile than irreligious people, and perhaps in the long run this will lead to increased religiosity in society. Groups like the Haredim being the beneficiaries appears to be a specifically Jewish phenomenon.
