In the United States, at least, there is an absolute right to burn books. Or flags. If some Muslims take offense, hard cheese. If some Muslims take to murder and mayhem because someone may have offended them, hard cheese. That, apparently, is the nature of Muslims: prone to violence; not prone to controlling their own tempers.
As for why there must be no “looking into” the burning of a book, any book, here’s the only relevant text:
Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.
We Americans call it the First Amendment to the Constitution, Harry. You ought to familiarize yourself with this document.