Pretty much what Siege said. The standard that she and I, and our church, goes by is that our duty as Christians is to follow the three or four laws that Jesus classed as most important, applying anything else in the Bible as it is mediated and interpreted by those laws. In other words, regardless of my own personal standards as to the morality of, e.g., eating shellfish, if I see someone else (say gobear) eating oysters, I should react, not with the view that God prohibited doing so in Leviticus and I am therefore obliged to correct gobear of his sin, but rather follow the Second Great Commandment, the Golden Rule, and similar guidance in how I ought to behave toward him. She and I, and skammer, Baker and a few others, are sworn before God to “seek and serve Christ in all persons, loving your neighbor as yourself” and to “strive for justice and peace among all people, and respect the dignity of every human being.”
Substitute “having gay sex” for “eating shellfish,” and nothing changes but the details; the principles on which we are to act are identical.
To be completely thorough, though, it is only fair to explain the conservative Christian stance, which Siege and I do not hold to, in terms that do not misrepresent it.
First would be the idea that there are absolute values of sin, specified in Scripture. And it is the right and duty of the Christian to attempt to bring other sinners to salvation by convincing them of their sins and the need to repent and accept Christ. If necessary, leaving those who insist on sinning to stew in their sins if they prove recalcitrant to this, it becomes necessary to influence society to remove from the ambit of legal, protected acts the commission of such sins, in order to protect others from being influenced to commit them.
Now, how do acts such as having/administering an abortion or committing gay sex acts differ from eating shellfish or wearing cotton/linen blend clothing? Simply that in this understanding, following Paul’s teachings, we are free from the Law of Moses, which cannot bring salvation – but not free to sin but rather free to live new lives in Christ. The dietary, ritual, and similar provisions of the Law are therefore not binding – but the moral code underlying them is. In general, such moral strictures are addressed at least tangentially in the New Testament, and can be divined by Paul or James or somebody making reference to unrepentant sinners who commit acts that parallel the OT prohibitions.
This of course is not what either Jesus or Paul actually said, but it furnishes a basis on which conservative Christians may selectively determine what constitutes a violation of the moral law while ignoring the provisions of the dietary and ritual laws. (I’d be quite interested in seeing how this threefold breakdown of the Law stands as measured against the Talmudic classification of the Laws, by the way.)
For us, however, this perspective is dead wrong – not because it cannot be founded in Scripture, for it certainly can, but because it goes flatly against the behavior that Jesus taught was incumbent on His followers. Matters such as “Judge not, lest you be judged. For with the measure with which you judge you will also be judged.” The condemnation of the Pharisees for doing the same sort of legalistic interpretation of God’s commandments in Matthew 23. The underlying principle of the Parable of the Sheep and Goats: “Inasmuch as you have done this unto one of the least of these, you have done it unto Me.” And above all, what Jesus, following Hillel, insisted repeatedly was the core and full meaning of the Law: To love God with all of oneself, to love one’s neighbor as oneself, to act towards him or her as you would wish he or she acted towards you. Forgiveness, mercy, compassion…all that sort of thing.
Like the conservatives, we are selective in our interpretation of Scripture. Unlike them, we are following the direct commandment of Jesus in how to interpret it.
Finally, to address the last paragraph of the OP, there are probably as many schools of thought as to the inspiration of the Bible as there are people who have given it any thought. The idea of direct verbal inspiration is merely one of them, and not one held by even all conservative Christians. Most people see God’s message being gotten across in bits and pieces by His efforts to influence fallible human beings who could each accept one small piece of it, and promulgate that piece in their writings. So we see stuff like Leviticus as being the Israelite legal code attributed backwards to Moses as the lawgiver – just as the 26th Amendment, written in 1971, is considered part of the Constitution written in 1787 and ratified in 1787-89. We see Paul addressing the culture and conditions of Corinth and Colosse at the time of writing. And we do not blindly and legalistically take a given passage as binding in the particular language used in addressing what was significant there and then as carrying over to a different culture and situation today. Paul’s quite vehement – and justified – condemnation of those who enslaved boy prostitutes in Corinth and those who hired their services has little to do with what matt_mcl and Potter, or Mr Visible and his partner, feel towards each othe today.