"If a man marries his sister, his father’s daughter or his mother’s daughter, and they have intercourse with each other, that is disgraceful; they shall be publicly cut off from the people; the man shall bear the penalty of having had intercourse with his own sister" (Leviticus 20:17*).
That seems pretty straightforward, and few would care to dispute it. Incest is unacceptable and isn't permitted. The trouble is that Abraham, a heralded "patriarch" of ancient times, married his half-sister.
"Besides, she really is my sister, but only my father’s daughter, not my mother’s; and so she became my wife" (Genesis 20:12).
This was a fact that I never had too much trouble with as an evangelical, because I simply reasoned that Abraham and Sarah purportedly lived hundreds of years before the Law came along. They were under a different covenant, one that didn't account for this kind of incest. I have more trouble with that reasoning now, and not just because if the Bible were to be taken as describing concrete fact, all of Adam and Eve's children committed incest. What we find in the Bible as we read it is a certain flexibility.
"Keep my statutes: do not breed any of your domestic animals with others of a different species; do not sow a field of yours with two different kinds of seed; and do not put on a garment woven with two different kinds of thread" (Leviticus 19:19).
In modern terms, this would mean that no mules should be bred, and that I'm a hopeless sinner because I like to plant sunflowers and maize together in the same rows. Very few Christians in our time would consider these rules they're meant to follow. Some rationalize it by saying that only certain laws from the Old Testament still pertain to the church, and others by taking the position that the new covenant superseded the old. What I see is a flexibility over time, as norms change and people begin to see things differently.
"Any man who prays or prophesies with his head covered brings shame upon his head. But any woman who prays or prophesies with her head unveiled brings shame upon her head, for it is one and the same thing as if she had had her head shaved. For if a woman does not have her head veiled, she may as well have her hair cut off. But if it is shameful for a woman to have her hair cut off or her head shaved, then she should wear a veil" (1 Corinthians 11:4-6).
Now there's a fun little passage from the New Testament. Clearly women are to cover their heads in some way when they are pray. Presumably they should do this throughout the church service. Indeed, I have encountered both fundamentalist women from the Dominican Republic and traditional Roman Catholic women in the United States who wear a scarf on their heads in church. Shouldn't all women do this? The passage in question is one that evangelicals choke on, sputtering excuses such as saying that it was a local requirement because of temple prostitution, or some such. The trouble with that excuse is that the text goes on to make it sound pretty universal.
"But if anyone is inclined to be argumentative, we do not have such a custom, nor do the churches of God" (1 Corinthians 11:16).
There are similar verses in there about women keeping silent in the churches, but those generally get ignored as well. If anything they are applied in the sense of not letting women be ordained as pastors, as is now the case in the Southern Baptist Convention. That, even though the text is clear that women aren't even supposed to ask questions at church.
The fact is that there exists with every Christian religious group a canon within the canon. The Bible is their overall canon, but the parts that they really emphasize are their canon within the canon. The Bible is really a book of many writings (66 in the Protestant Bible, and 72 in Catholic Bibles) and speaks with many voices. Which voices get heard depends on the person or people who are listening. Thus we have churches that are adamant, for example, that women shouldn't be clergy, and others that ordain them freely. Likewise, many Christian denominations ban or limit LGBTQ+ people from involvement at all or some levels of their churches, while others welcome people of diverse sexualities and gender expressions in every capacity for which they are gifted.
Now, I'm not arguing in favor of allowing incest. Sisters and brothers, like all near relatives, must not be sexually involved with one another. That just stands to reason. As is always the case, we don't actually need the Bible to know what is ethical and reasonable. We instead need to combine careful thought with empathy and compassion to build our ethics. From a scientific, sociological, and psychological perspective it should be readily apparent that certain sexual relationships are simply not acceptable, even between consenting adults. At the same time, that doesn't preclude consenting relationships that pass the ethics and science test, even if some people (i.e. homophobes) find them "icky."
We live in an age of right and wrong, black and white, yes or no. Nuance is not understood or appreciated. And yet, the Bible demands a nuanced approach that understands both holding things in tension and letting some things go. The Bible was written and redacted by many people in vastly different circumstances and centuries. Sometimes its various parts agree, and other times not so much. So it stands to reason that someone reading it should be willing and able to bring their own perspective to it as well. Perhaps in the end the discordance is more of a feature than a bug.
*Scripture quotes are taken from the New American Bible, Revised Edition.