One of the trajectories I notice when I look at the history of Christian influence on society is a broadened conception of who counts as human or truly human. We see it explicitly in Jesus when he talks about love of enemies. We see it in the apostolic church when they moved beyond Israel. In more recent history we see it in the abolitionist and civil-rights movements. Many acted like non-whites were not fully human. Yet under the influence of Christianity (though in conflict with some Christian traditions), our broader culture has been gradually influenced to the point where non-whites are counted by most people to be truly human.
I am not an expert on the history of abortion, but I know that our first records of church teaching against abortion are very ancient - at least as old as the Didache (which is early 2nd century in origin). In more recent times (I'm thinking of 19th & early 20th century US) there wasn't a lot of concern about abortion - but why should there be? Margaret Sanger & crew didn't start their eugenics program until the 20th century and took a long time to devalue the unborn child. Their propaganda led to a cultural regression in this area, in alliance with the modern commitment to convenience. Many Christians have stood up against this devaluation and the abortion-culture it produced, some by simply arguing against abortion as murder, others doing so explicitly in the name of a Christian commitment to a broader conception of who is truly human, yet others coming from the point of view of seeing evil in the culture of radical individualism and the convenience it requires.
As to capital punishment, murder & killing, we see it all in scripture. We see capital punishment commanded for a number of crimes: murder, witchcraft, improper sexual practice, disobedience to parents, etc. Usually in current discussions, as far as I can tell, capital punishment is only encouraged for the first of these crimes (if my perception is wrong, some of you supporters correct me), though apparently Caesar is free to declare other crimes as worthy of death (horse thievery and treason come to mind).
I can imagine homosexuals (for example) seeing the OT command to put them to death, hearing Christians say we need to believe and obey the whole Bible, coming to believe that Christians want to kill them. Caesar currently doesn't consider homosexuality as worthy of death, but calls to Christianize Caesar can be heard as encouragement in that direction. This is one reason I don't think the allowance (or shall we say COMMAND) of capital punishment in the OT should be relied upon for arguing the righteousness of Caesar practicing the same today. Sure there are no clear, explicit, unambiguous commands in the NT to do away with capital punishment. Also there are no NT commands to cause Caesar to narrow the scope of capital punishment to certain types of murderers only, letting people guilty of sexual deviancy, idolatry & disobedience to parents off the hook.
Are there some who want to argue that the Christian tradition has wrongly exerted its influence in recent times to narrow the scope of Caesar's application of capital punishment? Are there some who argue for a return to full obedience to the OT in this area, perhaps because they see no NT command to do otherwise? Such arguments seem to leave the crucified Son of God far behind.