Time evolves. Science moves on. Why not religion?
This is quite a mind-provoking question, and there is no perfect answer to your question.
In fact, religion is moving too. You can google for some topics like new age movement you can find many people are trying to so-call keep up religion with modern thinking and science. Some quasi-religions (for lack of vocabulary I use this term), like Confucius which was ban during Mao Tze Tung's time in China is coming back. Many Chinese have given great respect to this greatest philosopher so much so that Confucius was worshipped at. In China you can see quite a number of Confucius temples.
For Christians - like myself - who are Bible-believing, God is unchanging; He is the same yesterday, today and forever; heaven and earth will pass away but the Word of God is everlasting.
Quite to the contrary, I (and I believe many Christians) find it puzzling why should God keep up with time. He is the Creator of everything and God is outside time.
As I have mentioned earlier, there are many so-call new age movement churches especially in the U.S. trying to introduce doctrines and teachings outside the Bible and this has caused a lot of confusions among Christians and non-Christians.
I cannot speak for other religions but I believe Buddhism is too changing. For example, the practice of cell-group by Christians to study the Bible is now too imitated by some Buddhist groups and they too have used Christian music and hymns and substituted with of course the words with the Buddhist scriptures. To me, this is like a new age movement by the Buddhists trying to keep up with time. As we can see that a Buddhist monk who is supposed to live simple life have dozens of credit card and openly declared that devotees can't expect monks to live like before. They too are human and they too need some enjoyment, so was his opinion. I don't think monks of the 3rd century would dare to say any of this. So time have changed and monks are trying to keep with the the modern world - for better or worst?
On your questions of "Why do you all believe in 3rd century books", I presume you are asking specifically why Christians believe in the Bible. Just by way of note, Bible is divided into the Old Testament and the New Testament. The oldest book in the Bible is generally agreed by bible scholars to be the Book of Job which was written more than 4000 years ago and most of the New Testament's scriptures were written between AD 40 - AD 100. So, why should such old books still believed by so many people and have such great influence on people's lives?
For Christians, our answer is simple - because this is God's divine message to the people on earth and even though there are many people trying to destroy this book, the Bible, but time has shown that it is undestructible. There are more books and commentaries written about this book than any other books. This book, the Bible, is translated to over 2,600 languages and dialects and the translation to other languages is a continuing process. It will never be destroyed.
The second reason is that this is a historical book. Many of the places and people's names listed or mentioned in the Bible have been discovered or confirmed by archeologists to be true. It is not a book of fables or legends or myths.
The third reason is that the discovery of the Dead Sea Scrolls in 1947 has shown that this is a book that has been preserved for many thousand of years in terms of accuracy of transmission. No other book has this same quality of preservation. Go to the Google and search for the key words like Dead Sea Scrolls and you can see many articles on this.
The fourth reason is that the prophecies and predictions in the Old Testament have given great creditability that the Bible is not just a book. It is a book that accurately foretells the future - and our future in this world if anything can go by, is going to be very ugly. It is alredy getting uglier and uglier by the day. But God has foretold us that there is going to have an everlasting kingdom that will replace this sin-sick world of greed, of lust, of pride. God Himself will rule this kingdom as the King of kings and Lord of lords.
God Bless