In the comments Europeans often point out that nations we Americans consider very secular, such as the United Kingdom and the Netherlands, actually provide state subsidy to religious schools. Part of the issue here is that Americans have a caricature of Europeans in mind, just as Europeans often have a caricature of Americans. Though in terms of their personal beliefs most Europeans are more secular than most Americans, that does not mean that we Americans can infer from that particularities of how Europeans organize their relationship between church & state. When the American republic was founded a proactive effort was made to separate the national government from any particular church or religion (a precedent which was eventually followed by the states in the early 19th century). At that time even nations with a reputation for religious tolerance, such as the Netherlands, arguably treated their minorities as what we would recognize today as “dhimmis” (see Divided by Faith: Religious Conflict and the Practice of Toleration in Early Modern Europe).
And yet despite the lack of national promotion of one particular sect America remains an exceptionally religious nation, at least by belief. Most European societies took different tracks (I think one major confusion by Americans is the idea that there is one European outlook on particular questions). Which brings me to a weird historical oddity I recently stumbled upon: Newfoundland had a purely sectarian public school system until 1997. You can read about it here. This system seems to be what the Catholic Church would have preferred in the 19th century for the United States, as the public school system was strongly tinged with Protestant presuppositions (e.g., reading Protestant Bibles). In the United States the Church lost. In Newfoundland it looks like they obtained a satisfactory compromise.
(the title is a joke, Canadians supposedly have a sense of humor)