The First Amendment and the Religious Exception

The idea of a "religious exception", as commonly defended, is both heart-warmingly humane and oddly indefensible.  That citizens not be forced to do things they consider immoral seems like the most straight-forward common sense; that citizens be allowed to ignore the law of the land for any consideration is a legal absurdity.
In the United States' tradition, the most relevant article to cite is the first amendment to the Constitution, which states:

Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.

 Two things are most straightforwardly guaranteed here: in the first case that the Congress on the United States shall not proclaim any one religion, sect, or cult to be an official or favored one.  So far we have done a fairly good job on this score, and perhaps even gone overboard to the point of denigrating all religious considerations in political decision-making.

The second clause, though, causes more difficulty.  (It is worth noting in passing that the general reading of these amendments, while they bind Congress specifically, has included the other branches of government, Congress having been specially limited as the branch which set policy.)  We can quickly recognize that it has in fact not been consistently followed.  Until very recently, the most infamous clear violation of this principle would be the persecution and de facto outlawry which followed the early Mormons largely on account of their practice of polygamy.

This exposes the potential problem: if a country, collectively speaking, truly believes some action to be wrong - in a more modern context, we might cite the draft (or, I suppose, draft-dodging), or segregation - at what point do we say, "Enough is enough?"  The hard-line libertarian answer - allow everything! - is absurd.  Not only would it be rejected by almost any populace, even the proponent of the idea would not want to extend it to some things - a religion- or culture-driven "honor killing", for example.  And his objection would not necessarily be the death (if it were of, say, an already criminal murderer or rapist), but the essential lawlessness of the act, especially if the victim objected to the code (as we can all imagine most would).

In the current state of politics, when this principle is being challenged on a matter of life or death - contraception and abortion - I have to admit I am glad the law, interpretation, and precedent exist and stand mainly on the side I favor.  But in the long term, this seems an uneasy and impractical compromise.  There is a part of me that would be more comfortable without the exception, without that second clause and its interpretations, even if the result were to be requiring civil disobedience - which seems often the best way to change laws.