As a citizen, I must consider the whole, not just my private views. A society is a unity, and unless I offer what I render in service to that unity, and instead only serve myself - my private moral views, I actually violate my duties to the Divine Mystery. Again, in the Gospels, I am admonished to love my Neighbor as myself. In uniting the teachings from these two places, I can come to understand that Christ has made clear the distinction between the different realms and the different duties.
Now it may be, as Thoreau saw so clearly, that my higher duty will call upon me to sacrifice something of my own (such as my physical freedom), in how I render unto the State (Caesar), but nowhere is it suggested that I may compel another to sacrifice in order to force them to follow my own private moral views. The whole point of the bill of rights is to prevent a tyranny of the majority, whatever their morality or character.
I can then see how it is that my private moral duty requires of me, for example, to not commit abortion, and that it may require that I sacrifice my physical freedom, through civil disobedience, to oppose abortion, but nowhere does this allow me to impose my moral views and require a sacrifice of others, using the power of the State to compel them to share these views.
It is true historically that competing values have met and battled in the realm of Law making. But it is also true that we live in a version of the State in which the rights of the minority to freedom from the tyranny of the majority were clearly set forth in the Constitution. Freedom has no meaning at all, if the majority may at any time use the power of the State to impose its moral values. The only true function of the State is the creation of rules that apply to all, and are acceptable to all.
The compulsion of the Law (the power of the State) is not meant to be a substitute for the moral and religious freedom of the individual human spirit, in the following of its own conscience. Out of conscience I render unto God, but it is out of selfless compassion and love, that I render unto the State (Caesar). What I render unto the State is not about me, but about We - about the other - the Thou. The Preamble to the Constitution does not begin I, the Individual, but We the People.
There are those who might insist that they must do all they can to save the souls of others, a pernicious dogma that has historically destroyed more than it ever created. It assumes that the Divine Mystery has no purpose for the lives of the assumed unsaved, and that the imposition of my conscience on your conscience is a divine commandment. It is an enormous exercise of hubris and vanity to live out those assumptions.
It is this failure to realize these truths about the difference between the duties we owe Caesar (the State) and to the Divine Mystery, that has contributed far too much to the destruction of the Republic in our time. Even so, the wider realities about the forces assaulting our Republic is a whole other story.