Political correctness can, I believe, influence Bible translation in spite of contrary intentions on the part of translators. The influence mainly affects details of meaning, so it may not seem too serious at first glance. But in the end it threatens the vital doctrine of the plenary inspiration of Scripture.
Plenary inspiration means that the whole of Scripture—every detail of meaning, not just the main point or selected parts—is the Word of God. This doctrine comes from passages where Jesus affirms details of Scripture: "Not an iota, not a dot, will pass from the Law until all is accomplished" (Matt. 5:18 ESV); and from passages like Proverbs 30:5: "Every word of God is flawless" (NIV). In addition, the Bible indicates that we are under the authority of Jesus as our master, who speaks to us through the Bible. Choosing which details in Scripture we will accept makes us the master instead, undermining our relation to Christ.
Father in Hebrews 12:7
Now political correctness puts pressure on translators to change details of meaning that do not fit modern egalitarian (or feminist) expectations. How? In Hebrews 12:7 the New International Version says, "Endure hardship as discipline; God is treating you as sons. For what son is not disciplined by his father?" The TNIV changes the last part: "For what children are not disciplined by their parents?" The underlying Greek word is pater in the singular, which means "father," not "parent," and certainly not "parents."
The official TNIV website nevertheless posted an essay defending this choice, arguing that it avoids misunderstanding: "Was he [the author of Hebrews] suggesting that girls never need disciplining?
Or that a mother never should discipline one of her children, ...