Thanks for your question, it is a good one. You are picking up on an important aspect of reading the Bible, which must form part of our interpretive process. Let me try to explain below briefly.
Firstly, there are a number of reasons Christians have come to believe the Bible is relevant; here are a few that come to mind immediately:
(1) The believability of Jesus.
Christians are persuaded that the central person of the Scriptures (Jesus, who is the full revelation of God in history) is who he said he is. That is, the who at the center of the Scriptures is true and significant and therefore what is said about him is utterly relevant to all people at all times.
(2) It accurately describes the state of the world.
If we came to the Bible and it said things like ‘up is down’ or ‘murder is a virtue’ we would rightfully feel it was giving us a false picture of reality. But this is not the case. What we see is it talking about an initial state of innocence (creation), a departure from this intended design (the fall), an intervention to put things to rights (redemption) and a day when all will fully be put right (new creation). All this accords with what we see and long for as human beings.
(3) It’s claims can be tested historically
We can actually weigh what is said in the Scriptures with what evidence external to the Bible (e.g. other historical documents, treaties etc.) This includes claims about various nations, places, building projects, wars, materials, names, lineages etc. When it comes to Jesus, his life, ministry, death and resurrection are claims that can also be weighted for their historical probability. When this is done, it is clear that the Bible plays an important part not just in providing revelation, but revelation in history.
(4) The biblical documents can be historically verified.
How the canon of Scripture came together is a historical process that we can test and trace back to the earliest witnesses to the life, death and resurrection of Jesus (without doubt the most central figure in all history). The preservation of the apostolic proclamation found in the Scriptures makes the Bible very relevant. But even if one doesn’t accept the Bible as telling a true story, even the historical importance of Jesus to human history makes it relevant.
(5) The Bible and Jesus testify to the relevance of the Bible.
Here Scriptures like 2 Peter 1:20-21 and 2 Timothy 3:16-17 come to mind, which attribute the writing of Scripture to the prior inspiration of God’s own spirit. Jesus also has an incredibly high view of Scripture (e.g. John 10:35). The Bible possesses truths that are ‘eternal’, in that they describe the truth about the eternal God. What is true about this being will always be relevant.
(6) Its power is evident in individual lives today
People are still encountering the truth recorded in the Bible in the 21st century in powerful ways. This point alone should give us pause to admit its relevance in our society and personal lives. People are meeting Jesus, which means the Bible’s importance is not stuck somewhere in 1st century Palestine.
But here we come to the point you were hinting at regarding interpretation. While the the Bible possesses God’s eternal truth, it also comes to us through a particular historical period. The interpretive pattern that we need to follow, then, is to glean the biblical principle without getting stuck in particular cultural customs into which certain texts were written (there are, of course, some texts that are very clear, e.g. “Do not get drunk on wine”). Others require greater cultural flexibility: for example, greeting each other with a ‘holy kiss’ would have been entirely appropriate in Paul’s day, but in many cultures today it is not. What we take from this command is to be warm and hospitable to brothers and sisters in the church. If we take the heart of the principle and apply it to our current contexts, the Scriptures remain absolutely relevant.
Let me give the last word on this point to Gordon Fee:
“Because the Bible is God’s Word, it has eternal relevance; it speaks to all humankind, in every age and in every culture… But because God chose to speak his Word through human words in history, every book in the Bible also has historical particularity; each document is conditioned by the language, time and culture in which it was originally written.”
- Gordon D. Fee and Douglas Stuart, How to Read the Bible for All Its Worth (2005), p. 21.