Book burning is one of the great insults to any religion or ideology. In July 2010, pastor Terry Jones even made international news, sparking outrage, when he announced he would be burning 200 Qur'ans in response to Islamic terrorism. More recently (and more personal to me), I found a post in a group in which a member had received a copy of "Tony Blair A Journey" as a gift, and asked what should he do with it. Most people, not surprisingly given the content of the group, suggested destroying or getting rid of the book in some way. Bin it, burn it, use it as toilet paper. My suggestion? Read it.
Morally speaking, there is nothing wrong with burning a book. Even if you burn a Bible, what matters isn't the act, but the motive behind it. If you burn a Bible because you hate God, the sin is your hatred of God, not burning the Bible. If your motive is the destruction of a poor copy/translation, that's actually quite pious. Thus, the destruction of less Holy books isn't objectively evil either.
However, there is always the practical element of how you treat books. For example, just as your motive for destroying the book determines the morality of it, so also does the act of destroying the book tell those who believe it how you see their beliefs, and in many cases, even how you see them as people. This, of course, is understandable. Most of the time, people aren't trashing books out of love. Think about it: Every time you so much as joke about burning a book, is it out of love for the believers, or hatred for the ideology? Maybe even the believers themselves?
As Christians, we are commanded to reach out to people "with gentleness and respect" (1 Peter 3:15). When we trash books, or even speak (unnecessarily) ill of an ideology, we're not doing this. Rather, we're stirring up anger, and even hardening hearts. This, of course, is not conducive to fruitful, soul saving discussion.
Some like to point to Acts 19:19 to justify book burning. This, once again, falls under book burning being morally neutral; your motives matter. In Acts 19:19, it wasn't the Apostles burning books as a show of disrespect to the believers, but the ex-believers burning their own books as an act of repentance. Their hearts had already been won. Just two chapters earlier, however, we see a good example of how to reach those whose hearts haven't yet been won:
"Then Paul stood in the midst of Mars' hill, and said, Ye men of Athens, I perceive that in all things ye are too superstitious. For as I passed by, and beheld your devotions, I found an altar with this inscription, To The Unknown God. Whom therefore ye ignorantly worship, him declare I unto you." (Acts 17:22-23).
Notice Paul's strategy. He doesn't storm into Athens and trash their sacred objects. Rather, he studies their religions, draws on elements of it, and uses that to make God known to them. We can do likewise today. If someone gives you a religious text, don't reject it, accept it gratefully, study it, discuss it with them, and use it to bring them to Jesus. By showing such love, and a will to engage, you potentially bring them to Christ.
Now, am I saying we must respect false views? Absolutely not. If something is wrong, reject it, criticise it, seek to lead people out of it, and make no apologies if they unjustly take offence. But remember, false worldviews can do no harm to you on their own, they can only harm the believers. Books are not bombs, even the worst of them can be gifts, aiding you in your quest to bring the lost to Christ. It may not always work. Indeed, Christ Himself warned that we are likely to endure persecution for preaching Him. But I can guarantee this much: You will reach far more people by seeking to understand them than by being so absorbed into preaching the Gospel, you neglect to actually live it.
As Christians, we've been given a charge. It is a challenge, but also a privilege, for as Christ says, if the people are silent, even the rocks can cry out (Luke 19:40). God doesn't need us, and He would lose nothing, first of all if we were condemned, but even if He took us home the minute we were converted. Every minute we breathe is a blessing, to the point where the Apostles would rejoice even when they were scourged for the Gospel (Acts 5:41). In other words, there is no sense in which false worldviews can harm us, for even our losses are great profit to us. How, then, can we hold hatred in our hearts, even for those whose very riches will not follow them to their graves?
Book burning, and similar acts, are morally neutral. Your motives matter. For purposes of witnessing, even the most grotesque of religious texts may be more valuable to us intact than in pieces. Therefore, take what Satan meant for evil, and use it for the glory of God. Take the Qur'an, place the Book of Mormon on your shelves, do no harm to the Catechism of the Catholic Church. Whatever the work, read it, cite it, let God's word crush it with your gentle tongue. That way, we change minds, hearts, lives, and grow the Kingdom of God to such an extent that when an evil book is burned, it is out of love for God, rather than hatred for those made in His image.