You're just playing a game. You're still trying to use the king's sword to make pagans act like Christians.
The US was never a Christian nation. It is a nation with a lot of Christians in it, and it is a nation that was set up to follow 1 Timothy 2, to allow Christians to "lead a tranquil and quiet life in all godliness and dignity."
But to be a "Christian nation" it would have to have Christian national policies, and that has never been the case, not from the first day.
America still does have the king's sword, even if not a king wielding it, and it includes every citizen into the process of making the laws that decide upon whose necks that sword shall fall. The purpose of a sword is not to enforce Christianity, but to make a society that is liveable and fair for everyone.
Nobody is forced without having a say. Pagans are part of the decision making process of where the sword shall fall, as are Jews, and as are Christians. There is a democratic element in determining the laws, which gives Christians a very strong say in writing the laws that will govern us all. Checks and balances have been set into place against this too, to ensure that no church becomes supreme, and that all religions and even non-religions are treated with respect. That in no way detracts from the idea that American culture and society is imbued with Christianity that is reflected into the sensibilities of its institutions.
Theocracy in a pluralistic world is not a distinctly Christian sin. It has been a problem for every people who seek to govern a pluralistic population.
America has developed a free system, in which everyone gets a say, and this includes Christians, who are still in the majority. Christians ought not be expected to defer their influence on account of being in the majority. After all, laws are still necessary, and laws that differentiate in terms of race, creed or colour are assuredly not the way to go. Justice, to be justice, must be blind to all of that.
Fortunately, it is not as if pagans and Christians and Buddhists and Jews inhabit completely different universes when it comes to morality. Morality after all is not relative. It is an absolute. If rape is wrong for a Christian, it does not therefore become right for a pagan. There are rational arguments that can be made to appeal to the moral sensibilities of all people who have been imbued with a conscience that precedes the development of any religious doctrine. Jews, for example, fully understand that religious strictures that define their religion, such as shellfish laws, are reflective of their own practices, and not elements of a universal morality- even as laws regulating the humane slaughter of food animals does have something of the universal about them. Likewise, Christians are aware that Sunday as a day of rest is a convention and not a moral imperative, even as a day of rest does have a universal moral appeal that recognizes that people are more than what their occupations define them to be. Sunday as an American day of rest does not therefore make America a theocracy with sword firmly planted against the necks of others with different sabbaths set aside, but a country with Christian conventions as part of their institutions.
Morality, even in a pluralistic society, is possible. That is not theocracy, but just common sense.