How the First Amendment Came to Be

James Madison is considered the father of the First Amendment. The Library of Congress gives this background (with boldface added by me):

James Madison took the lead in steering such a bill through the First Federal Congress, which convened in the spring of 1789. The Virginia Ratifying Convention and Madison's constituents, among whom were large numbers of Baptists who wanted freedom of religion secured, expected him to push for a bill of rights. On September 28, 1789, both houses of Congress voted to send twelve amendments to the states. In December 1791, those ratified by the requisite three fourths of the states became the first ten amendments to the Constitution. Religion was addressed in the First Amendment in the following familiar words: "Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof." In notes for his June 8, 1789, speech introducing the Bill of Rights, Madison indicated his opposition to a "national" religion. Most Americans agreed that the federal government must not pick out one religion and give it exclusive financial and legal support.

Note that no one was trying to keep religion totally separate from government. The clear focus was to keep the Federal government from selecting one religion over another. In the USA at that time, the desire more specifically was to keep the Federal government from choosing any one Christian denomination over all the others as a national religion.

Learn more at the Library of Congress