Obiter Dictum - Latin for "something said in passing." Thanks, I know.
The fact that America is a Christian nation is the basis for the Court's interpretation of the statute in question; it is not "dicta."
It is very much dicta - the court's legal reasoning ends with "We find, therefore, that the title of the act, the evil which was intended to be remedied, the circumstances surrounding the appeal to congress, the reports of the committee of each house, all concur in affirming that the intent of congress was simply to stay the influx of this cheap, unskilled labor", and the sailing off into flights of fancy begins immediately thereafter. The basis for the holding was the legislative history of the bill in question. What comes after that is simply Brewer mugging for the crowd, with no precedential value whatsoever.
PUBLIC CITIZEN v. DEPARTMENT OF JUSTICE, 491 U.S. 440 (1989) - The Church of the Holy Trinity entered into a contract with an alien residing in England to come to the United States to serve as the director and pastor of the church. Notwithstanding the fact that this agreement fell within the plain language [491 U.S. 440, 474] of the statute, which was conceded to be the case, see ibid., the Court overrode the plain language, drawing instead on the background and purposes of the statute to conclude that Congress did not intend its broad prohibition to cover the importation of Christian ministers. The central support for the Court's ultimate conclusion that Congress did not intend the law to cover Christian ministers is its lengthy review of the "mass of organic utterances" establishing that "this is a Christian nation," and which were taken to prove that it could not "be believed that a Congress of the United States intended to make it a misdemeanor for a church of this country to contract for the services of a Christian minister residing in another nation."