What does the problematic notion of rights and how it has been construed in modernity mean for Christian ethics? Allow me to make some summary and concluding statements.
First, the notion of unalienable rights comes to the forefront of moral and philosophical thinking precisely as an attempt to avoid the arbitrariness of the modern attempt to develop a "universal" morality free from particular historical constraints. That unalienable rights are themselves arbitrary is seen in the fact that there are no criteria for deciding what is and is not a right. To say, "I have a right!" is tantamount to exclaiming, "I want this!"
Second, modern universal morality was no less bias and particular than the theological doctrines that were rejected as having moral significance. The modernist reading of history was not only slanted, it was disingenuous.
Third, modernist moral accounts are vague and unhelpful. In the attempt to deduce universal by rejecting particulars, moral reflection was stripped of any profound significance and public discussion became nothing more than pitting one's so-called rights against another.
Fourth, In attempting to relegate doctrine to the sphere of the private, theology was made unnecessary for ethical reflection. Indeed, it was seen as a hindrance. Thus, Christians were basically told that they could participate around the table of ethical discussion in a pluralistic society only if they left their particular theological convictions outside the room. What Christians must insist on instead, is that they participate in the discussion as Christians, and expect as well that Muslims will participate as Muslims and atheists participate as atheists, etc. It is only in bringing the particulars together around society's table of discussion that true pluralism can exist and flourish. Insofar as Christians assume rights language as the context of moral reflection and take up such language, they will effectively take themselves out of public moral discourse as Christians. Rights language is not Christian language.
Fifth, Only when theological convictions are also construed as moral convictions can theology and ethics be adequately explicated. Rights arguments are contentions that operate on the false assumption that there is such a thing as a general universal (i.e. timeless and ahistorical) ethic. Christian ethics is not based on rights, but a particular people's history, and the God who has called them into existence through the life, death, and resurrection of Jesus Christ. This is, of course, a universal claim. There is nothing more universal than the belief in the Lordship of Jesus Christ, but it is a Lordship rooted in particular convictions about a particular individual and his people. There is no stripping the context out of this claim and watering it down into some "universal" and "timeless" principle or right free from historical constraint. It is a relevant theological conviction and a germane moral conviction as well.
Ethics is a mode of theology. Doctrine has moral implications. For Christians, there is no getting around this. It is what it is.