Not very, one might argue. Back in 1984 then-governor of New York Mario Cuomo gave a speech in which he outlined his ideas about how a Catholic politican who personally believed that things like abortion and divorce are wrong should approach their responsibilities towards a public comprised of Catholics who agree, Catholics who disagree, and non-Catholics who might disagree or agree. When should a politician attempt to impose their religious beliefs and doctrines on others?
[M]ust politics and religion in America divide our loyalties? Does the “separation between church and state” imply separation between religion and politics? Between morality and government? Are these different propositions? Even more specifically, what is the relationship of my Catholicism to my politics? Where does the one end and other begin? Or are the two divided at all? And if they’re not, should they be?
This is a very good question. All politicians have moral beliefs which influence how they vote and what sorts of laws they favor. That does not mean, however, that sectarian religious doctrines should be used as the basis of civil law and public policy:
Must I, having heard the pope renew the church’s ban on birth control devices, veto the funding of contraceptive programs for non-Catholics or dissenting Catholics in my state? I accept the church’s teaching on abortion. Must I insist you do? By law? By denying you Medicaid funding? By a constitutional amendment? If so, which one? Would that be the best way to avoid abortions or to prevent them?
I can, if I wish, argue that the state should not fund the use of contraceptive devices not because the pope demands it, but because I think that the whole community—for the good of the whole community—should not sever sex from an openness to the creation of life. And surely I can, if so inclined, demand some kind of law against abortion not because my bishops say it is wrong, but because I think that the whole community, regardless of its religious beliefs, should agree on the importance of protecting life—including life in the womb, which is at the very least potentially human and should not be extinguished casually. No law prevents us from advocating any of these things. I am free to do so.
In other words, as a Catholic in his private life he can reject abortion because of what his bishops say, but as a politician it would be wrong for him to try and direct public policies based upon what his bishops say. If the bishops can convince a majority of people that abortion or divorce are wrong without relying upon Catholic doctrine, then perhaps the position can be advanced in the law - not because it is Catholic, but for independent reasons. This is because a Catholic politician, when acting as a politician, must represent all citizens:
[T]he Catholic who holds political office in a pluralistic democracy—who is elected to serve Jews and Muslims, atheists and Protestants, as well as Catholics—bears special responsibility. He or she undertakes to help create conditions under which all can live with a maximum of dignity and with a reasonable degree of freedom; where everyone who chooses may hold beliefs different from specifically Catholic ones, sometimes contradictory to them; where the laws protect people’s right to divorce, to use birth control, and even to choose abortion.
In fact, Catholic public officials take an oath to preserve the Constitution that guarantees his freedom. And they do so gladly. Not because they love what others do with their freedom, but because they realize that in guaranteeing freedom for all, they guarantee our right to be Catholics: our right to pray, to use the sacraments, to refuse birth control devices, to reject abortion, not to divorce and remarry if we believe it to be wrong.
The Catholic public official lives the political truth most Catholics through most of American history have accepted and insisted on: the truth that to assure our freedom we must allow others the same freedom, even if occasionally it produces conduct by them which we would hold to be sinful. I protect my right to be a Catholic by preserving your right to believe as a Jew, a Protestant, or nonbeliever, or as anything else you choose.
We know that the price of seeking to force our beliefs on others is that they might someday force theirs on us. This freedom is the fundamental strength of our unique experience in government. In the complex interplay of forces and considerations that go into the making of our laws and policies, its preservation must be a persuasive and dominant concern.
Freedom exists for everyone, not simply for those who have the "correct" religious beliefs. If Catholic leaders use their religious authority to intimidate politicians into voting a certain way, then they are undermining the basis for their own freedoms because they are effectively forcing politicians to adhere to something other than their public duty to the Constitution. The freedom of Catholics in America to go to their own churches is not a creature of Catholic doctrine but of the same laws which protect the freedom of others to go to divorce court, to go buy condoms, and to go to an abortion clinic.
Then there is the question of whether criminalizing abortion is even the best way to advance a pro-life position. Cuomo argues that while Catholicism demands one be pro-life, it doesn't stipulate a particular legislative means for promoting that pro-life ideal:
I repeat, there is no church teaching that mandates the best political course for making our belief everyone’s rule, for spreading this part of our Catholicism. There is neither an encyclical nor a catechism that spells out a political strategy for achieving legislative goals. And so the Catholic trying to make moral and prudent judgments in the political realm must discern which, if any, of the actions one could take would be best. ... Approval or rejection of legal restrictions on abortion should not be the exclusive litmus test of Catholic loyalty. We should understand that whether abortion is outlawed or not, our work has barely begun: the work of creating a society where the right to life doesn’t end at the moment of birth, where an infant isn’t helped into a world that doesn’t care if it’s fed properly, housed decently, educated adequately, where the blind or retarded child isn’t condemned to exist rather than empowered to live.
I've quoted a lot from Cuomo's speech and I hope he doesn't mind, but there was so much to choose from - I recommend reading the original because there is more interesting things there. It puts a very different perspective on the calls for Catholic politicians to "toe the line" which Catholic bishops are demanding. The idea that a Catholic politicians can't be a "good Catholic," be pro-life, and refuse to support criminalizing abortion doesn't seem very sound anymore.