Here are a couple of paragraphs from the Federalist Paper #2 written by John Jay. The main thrust of the paper is that a union should be formed. These give reasons why such a union would have a lot going for it.
In regard to the characteristics of the people, notice that what is stressed here is the lack of reasons for disagreement rather than the virtue of being English and speaking English and so forth. Jay would doubtless have written much the same had the country's inhabitants been Turks, except that the proposed form of the new government would certainly have been different. The key words here are same and similar. Therefore when Jay writes of the people professing the same religion he is not expressing any value judgement on religion, its necessity or irrelevance. He is merely eliminating it as a source of contention. There is nothing here to indicate that he thinks America should be governed by Christian principles.It has often given me pleasure to observe that independent America was not composed of detached and distant territories, but that one connected, fertile, widespreading country was the portion of our western sons of liberty. Providence has in a particular manner blessed it with a variety of soils and productions, and watered it with innumerable streams, for the delight and accommodation of its inhabitants. A succession of navigable waters forms a kind of chain round its borders, as if to bind it together; while the most noble rivers in the world, running at convenient distances, present them with highways for the easy communication of friendly aids, and the mutual transportation and exchange of their various commodities.
With equal pleasure I have as often taken notice that Providence has been pleased to give this one connected country to one united people--a people descended from the same ancestors, speaking the same language, professing the same religion, attached to the same principles of government, very similar in their manners and customs, and who, by their joint counsels, arms, and efforts, fighting side by side throughout a long and bloody war, have nobly established general liberty and independence.