We are not a Christian country, but rather a secular country with secular laws. Until relatively recently in our history, we had laws against sodomy. Prior to 1962, being convicted of sodomy was a felony in every state, with sentences ranging from lengthy imprisonment (up to life), hard labor, castration. That was when we when Christianity had a greater influence on our legal structure and yes...they were prosecuted.
Social and political theories of New England Puritanism are embedded in our common law.
In 1811, a year after John Ruggles publically slandered Jesus Christ and His mother Mary in a New York pub, he was tried and jailed for blasphemy. In his opinion on the ruling, Chief Justice of New York, James Kent, said, “The people of this state, in common with the people of this country, profess the general doctrines of Christianity, as the rule of their faith and practice; and to scandalize the author of these doctrines is not only, in a religious point of view, extremely impious, but, even in respect to the obligations due to society, is a gross violation of decency and good order.” The sentence seems harsh, even by nineteenth-century measures, but it asserted a legal connection between Christianity and American republicanism.
Attorney and jurist Joseph Story observed that Christianity was part of the common law. A virtuous people, said Story, believe that piety, religion, and morality are “indispensable to the administration of civil justice.” In his treatise on the Constitution, Story writes that the real object of the First Amendment “was, not to countenance, much less to advance Mahometanism, or Judaism, or infidelity, by prostrating Christianity; but to exclude all rivalry among Christian sects.”
See Joseph Story, Commentaries on the Constitution of the United States (Quid Pro Books, 2013)