To be sure, the question of the Christian's obedience to the civil magistrate would be pretty easy if the state were simply totalitarian. In other words, if conformity were commanded with all loopholes abolished, then in the spirit of Romans 13 we would just suck it up and "obey their lawful commands" (WCF XXIII.4).
But when the powers that be confuse the matter by actually inviting challenges to their authority when or if it is abused (such as the insistence of the Declaration of Independence that a government should be "abolished" if it fails to secure the rights of the people who established it), then that changes things dramatically.
Here's where the distinction between the ethics of the civil and spiritual kingdoms is so striking, and, further, what makes appeals for "civil rights" that are peppered with biblical language so troubling. When one quotes Jesus to bolster his demand for the better treatment to which he feels he is entitled, not only is he misconstruing his Christian liberty as civil liberty (contra WCF XX.1, 4), but he is demonstrating a woeful ignorance of the cross. If Jesus did not invoke his unalienable right not to be killed, and if "the servant is not greater than his Master," then who are we to appeal to him to avoid suffering? If the kingdom of God teaches us anything, it is that following Jesus means foregoing our rights for his sake.
But the kingdom of man does afford its subjects certain "unalienable rights" (at least in this country’s expression of it). If, therefore, we feel that those rights are being violated, and further, if we choose to fight for them, then appealing the Scripture while doing so would seem to do more harm than good.
"Carnal weapons for earthly warfare" – sounds about right....