No serious Bible reader always reads literally, if by "literally" we mean "at face value." They read poetry as poetry, history as history, parables as parables, and prophecy as prophecy.
They know, for example, that psalms are poetry and sometimes employ poetic license, so that when a psalm says that “the waves clapped their hands” and “the mountains skipped like rams,” serious Bible readers understand the language in view to be figurative, not literal, historical, or prophetic. The same with statements from Jesus like "If your right eye offends you, pluck it out" and "If your right hand offends you, cut it off." Those words do not mean that Jesus seeks a mob of one-eyed, left-handed Christians. They mean that He wants us to stop sinning.
That's not picking and choosing what we want the Bible to mean, and it's not reading literally. It's trying to read the text as the author intended it to be read, which is sometimes literal and sometimes not. The text itself, if you pay close and careful attention to it, will tell you. But it isn’t always easy.
Some Old Testament passages present readers with a similar challenge, namely knowing when you should read them as binding and when you should not. In this regard, I call to mind C. S. Lewis's helpful insight from his Reflections on the Psalms: Because they are pre-Christian, some Old Testament texts are also sub-Christian. That is, some Old Testament passages are meant to be preparatory for the coming light in Christ and are not permanent. They enshrine and require things not meant to be eternally binding. They might permit or require things less than morally perfect. For example, OT laws that tell us how to treat slaves are not yet fully Christian laws. Knowing that human beings are in God's image and that Christ writhed in agony on the cross for them, that He died for their redemption, means that they must not be treated as mere property to be bought and sold. Some things simply cannot be done well. Nor were they meant to be. Laws like this are meant for their own particular time and place, not for all times and places. Our difficult task is to discern which ones are which and to read them as intended, using every historical, grammatical, philological, archaeological, and theological tool available to us in so doing. While that decision is often clear, it sometimes is not. Discerning the case before us is never to be an exercise in arbitrarily picking and choosing based upon whatever we happen to prefer at the moment. No, it's trying very carefully to read the Biblical text as the author (and the Author) actually intended. For example, some Old Testament laws, both civil and ceremonial, are like that. We aren't always meant to be sacrificing white lambs, abstaining from pork, making a wave offering, or practicing the year of jubilee. Being omniscient, God knew full well when He gave such laws that the days of the tabernacle and the temple would come to an end. He knew that His Son would make the full and final sacrifice for sin in His body on the Cross and thus suspend any need for a continued temple sacrifice. Knowing that, He did not intend for us to consider his laws in this regard eternally binding.
It's part of what theologians sometimes call “the doctrine of progressive revelation:” God did not give us the Biblical text all at once. It came to us over many centuries and in at least two languages. The earlier portions lead to the later and sometimes yield to them when the later arrive, their intended task -- preparation for Christ and His truth – then being complete.
Think of it this way: Think of God as a very adept Teacher. He meets his students where they are, and not where they ought to be. If He insisted on meeting them only where they ought to be, He’d never meet any of them because not one of them is in that position. So He accommodates his teaching to their ability to receive. He meets them where they are and slowly moves them forward. The ancient Israelites were, so to speak, in spiritual grade school. In order to move them forward and to prepare them for His own coming into the world to live among them, God met them where they were and adapted His law to their condition in order to move them forward. The Old Testament has many passages of that sort, passages that reflect not merely the moral will of God, but that also reflect the moral waywardness and recalcitrance of the people with whom He is dealing.
Your second grade math teacher did the same thing – and it worked. When you were learning addition and subtraction, she might have permitted you to count on your fingers as an aid to your current understanding. She did not intend for that practice to last forever. But in second grade, it might have been an appropriate accommodation. It helped you to understand and enabled you to move forward from there. Later on, in eleventh grade, when perhaps you are doing trigonometry or calculus, you can’t be counting on your fingers. That time is past. But that doesn’t mean that what your second grade teacher permitted was wrong, only that it was preparatory and not meant to be lasting.
God’s laws are like that. Some are preparatory and temporary.
Jesus’ way of saying so was to point out to His hearers in Matthew 19: 3ff. that Moses’ laws regarding marriage and divorce in Deuteronomy 24: 1-4 were rooted in human hardness of heart, but that from the beginning it was not so, and that in the end it will not be so again. For now, however, while hardness of heart still reigns, Moses’ rules obtain. They have a limited time of application and enforcement. They are temporary, but real. They are real, but temporary.
To discern carefully the facts about God’s laws, and to do so under His guidance, is not a matter of merely picking and choosing as you prefer, but of carefully reading, analyzing, and applying the text as God intended, following wherever possible, the teaching and example of Christ Himself.