Eric Kaufmann crunches the numbers:
In the Muslim world, women most in favor of sharia law have twice the birthrates of Muslim women who are most opposed. Religious Arabs have the numbers to reap the electoral rewards from the Arab Spring. Meanwhile, Europeans and Americans who report “no religion” are leading the shift to below-replacement fertility. In most of Europe, the nonreligious average around one child per woman. In the United States, they manage 1.5, considerably lower than the national 2.1. This disadvantage is not enough to prevent religious decline in much of Europe and America today, but secularism must run to stand still.
Israel's Orthodox population is another example:
Israel's first Prime Minister, David Ben-Gurion, and the largely secular Zionist leadership assumed that the black-hatted, sidelocked Haredim were a relic of history. They gave the ultra-Orthodox an exemption from the draft, subsidies to study at yeshiva, and other religious privileges to make sure their anti-Zionism didn't dissuade the Great Powers from establishing a home for the Jews in Palestine. In 1948, there were only 400 Israeli Jews with military exemptions, many of which were not used. By 2007, that number had soared to 55,000. Meanwhile, the fringe of ultra-Orthodox pupils in Israel's Jewish primary schools in 1960 has ballooned: they now comprise a third of the Jewish first grade class.