I think this might turn on the distinction between the moral and political. Believers are personally obligated to that which is moral in faith and practice. But that doesn’t mean they are obligated to a political outlook or conclusion. So, Christian Jane mayn’t herself have an abortion, but she may vote or even make legislation contrary to this. As someone opposed both morally and politically to abortion, I’ll certainly grant that there is something obviously wrong with the sort of logic that opposes abortion morally but protects it politically (paging John Kerry). But the personal obligation a believer has is moral, not political or logical.
i) What is this "distinction" between the moral and the political? What is meant by these crucial terms? Considering that people vote and think according to political philosophies (whether they are good philosophies or well-worked-out ones is not guaranteed), it is interesting to note what one respected political philosopher says: "What is distinctive about political philosophy, however, is its prescriptive or evaluative concern with justifications, values, ideals, rights, obligations--in short, its concern with how political societies should be, how political policies and institutions can be justified, how we and our political office holders ought to behave in our public lives. . . .Political philosophy can thus be aptly characterized as a branch or an application of moral philosophy" (Simmons, Political Philosophy, Oxford, 2, emphasis original).
ii) In response to the claim that it is a sin to have an abortion (because it is murder?) but not to vote for other people to legally have one, this seems confused. May she drive her friend to the clinic and pay for the abortion? If so, may she pay for a hit man to kill her parents so long as she doesn't pull the trigger?
iia) Is not the 2K out of WSCAL "confessionalist?" Do not the Westminster Catechisms define what a violation of the 6th commandment looks like, to wit:
Q. 136. What are the sins forbidden in the sixth commandment?
A. The sins forbidden in the sixth commandment are, all taking away the life of ourselves, or of others, except in case of public justice, lawful war, or necessary defense; the neglecting or withdrawing the lawful and necessary means of preservation of life; sinful anger, hatred, envy, desire of revenge; all excessive passions, distracting cares; immoderate use of meat, drink, labor, and recreations; provoking words, oppression, quarreling, striking, wounding, and whatsoever else tends to the destruction of the life of any.
How can the 2Ker claim voting to make or keep legal the murder of children is not a sin??? Is their talk of "Confessionalism" mere lip service? Since I don't believe that it is, here's an argument from the Catechism:
 If you violate the sixth commandment, then you have sinned.
 Anything that tends to the destruction of the life of any human is a violation of the 6th commandment.
 Voting to make or keep legal the murder of children by abortion tends to the destruction of human life.
 Voting to make or keep legal the murder of children by abortion is a violation of the 6th commandment.
 Therefore, voting to make or keep legal the murder of children by abortion is a sin.
Now the 2Ker needs to deny the validity of this argument or the truth of one of the premises. If they can do neither, the conclusion follows of necessity.
iib) One way to see if a position is logically valid is to use the same form of reasoning and simply switch out some terms. Suppose there is an island with 20 Christians on it and 20 non-Christians. 19 of the non-Christians are taken in by an argument for the criteria of personhood that has as a troublesome consequence that one of the non-Christians does not meet the criteria. So they decide to kill this guy, call him Bob. So, they put it to a vote. 19 non-Christians vote to kill, 19 Christians vote to not kill (holding to Christian teaching about man). One Christian, Ruben, is a 2K guy, he finds it a good compromise to vote to kill Bob. What should the local church say of Ruben? What does this say of Ruben? Is Ruben morally guilty? Was Ruben's vote sinful? Furthermore, in keeping with what Steve Zrimec said, suppose Ruben believes, indeed is obligated to believe, that Bob is a human. What say ye of Ruben?
If the above is rejected and no relevant disanalogy is pointed to (and if that's your approach, try to think ahead because it won't be too hard to switch up elements of the above story to get around the points raised showing it's disanalogous), then one must reject the argument that voting for the murder of children isn't sinful. If one denies he must, and one finds no logical flaw, then one must deny logic. If so, then that's another defeater for the position. If a position denies validity, then that is a good reason to deny that position.
iii) What does it even mean to claim that a Christian has an obligation to be moral but not logical? That is just odd. First, there are rational obligations to be logical. Second, one has a moral obligation to be logical, to think rationally, to be consistent. This is why the Bible can speak of people sinning in their reasonings.
iv) I wonder what role Natural Law plays in all of this. Natural Law has been the 2Kers only response to the Theonomists who wonder how 2K can escape relativism. Governments are not the highest law that rules the kingdom of common grace, natural law is. If natural law entails some position on a matter, then do not both governments and Christians have a moral obligation to honor and bring about and maintain that position? If not, just what the heck is Natural Law? Something I know not what? What is its use? Is it simply a boiler plate platitude used to escape the charge of relativism but not really something to be taken seriously?