Those who think Christians should keep their moral views to themselves, it seems to me, are logically bound to deplore many praiseworthy causes, including the abolition movement, which was mostly the work of the evangelical churches courageously applying Christian ideas of equality to the entrenched institution of slavery. The slave owners, by the way, frequently used "don't impose your values" arguments, contending that whether they owned blacks or not was a personal and private decision and therefore nobody else's business. The civil rights movement, though an alliance of Christians, Jews, and nonbelievers, was primarily the work of the black churches arguing from explicitly Christian principles.
Double standard. The "don't impose" people make little effort to be consistent, deploring, for example, Roman Catholics who act on their church's beliefs on abortion and stem cells but not those who follow the pope's insistence that the rich nations share their wealth with poor nations or his opposition to the death penalty and the invasion of Iraq. If the "don't impose" people wish to mount a serious argument, they will have to attack "imposers" on both sides of the issues they discuss--not just their opponents. They will also have to explain why arguments that come from religious beliefs are less worthy than similar arguments that come from secular principles or simply from hunches or personal feelings. Nat Hentoff, a passionate opponent of abortion, isn't accused of imposing his opinions, because he is an atheist. The same arguments and activity by a Christian activist would most likely be seen as a violation of some sort.
I agree. It seems the very fact of some religious backdrop to a decision disqualifies it from the public square. As Leo points out, those who think this way have massive lacunae in their understanding of the shape of the modern world. Trying to squeeze moral positions out of the public square simply because they are religious is like cutting off the branch you are sitting on. We might as well disqualify murder, theft, adultery, etc.