Are church members required to be pro-life? (That is, opposed to legal availability of abortion). Or may they be pro-choice — (in favor of allowing abortion under the law)?
The church has taken a solid position on the morality of abortion itself. The church web site makes clear: “The Church opposes abortion and counsels its members not to submit to or perform an abortion except in [certain] rare cases.” However, this does not answer the question of whether members must oppose the existence of legal abortion.
There are certainly variations of the pro-choice argument which would run counter to church doctrine. Any theory that holds that human life is irrelevant (think Peter Singer), or that abortion is a moral good, seems to be contrary to church doctrine.
But many pro-choice positions are not based on the idea that abortion is a moral good or that life is irrelevant, but on other ideas which may not be in conflict with stated church doctrine. That is, there are positions which condemn the abortion itself but do not require that it be legally proscribed.
First, members might be pro-choice based on libertarian principles. There is a strong strand of libertarian thought in the church. The basic libertarian philosophy is that the government should enact the minimum required number of laws, and generally let people (and markets) make their own choices. Such a position is easy to reconcile with a pro-choice position on abortion. (This is not to say that libertarian arguments require a pro-choice stance on abortion. But, they seem to provide ground for a member to be pro-choice).
Second, members might be pro-choice based on standard liberal equal-protection arguments that laws against abortion are restrictive of women’s rights. While recognizing that the act is itself harmful, members could reasonably believe that society should not enact laws that have the practical effect of burdening women at a greater rate than they burden men.
Third, members could reasonably believe (as the cases state) that laws against abortion are an unconstitutional limit on the right to privacy. Again, such belief need not be a statement that the act of abortion is good. But it can be a belief that abortion restrictions are unconstitutional. (Many things may be required by the Constitution which we do not necessarily think are morally good).
None of these positions depend on assumptions or ideas that are contrary to church doctrine (such as a belief that human life is irrelevant or that abortion is morally good). Therefore, it seems that they are ways that a member could be a faithful, pro-choice Mormon.
Finally, it seems to me that church members have substantially more leeway to adopt a pro-choice position without running afoul of church doctrine than members of some other faiths. The church has consistently refused to proclaim that life begins at conception, and has even taken some acts, such as lukewarm acceptance of stem-cell research, that seem to imply that it does not. (See also this Slate piece about the political freedom that has given the church).
(For original comments to this post, including some very good observations on both sides of the political spectrum, see http://www.timesandseasons.org/?p=333#more-333).