Sure. Publishers routinely classify books by "frontlist" versus "backlist", that is, new books by well-known others that are expected to sell well for at least a short period of time, versus older books and books by unknown others that may sell but at a slower pace.
Books are routinely classified by the target age group.
Books are classified by when they were written: recent, 20th century, colonial era, middle ages, ancient.
In a totally different sense, books are routinely classified by their binding: paperback versus hardcover, or the method of binding, like perfect binding (glue) versus stiched versus wire, etc.
Bookstores routinely separate out oversized books.
There are all sorts of classification schemes. No classification scheme is inherently right or wrong or even good or bad of itself; it is useful or not useful for a particular purpose.
If your goal is to judge the ideological impact of books, it might make good sense to classify them as liberal versus conservative or atheist versus Christian versus Hindu. If your goal is to allocate space to store books in a warehouse, you probably want to classify them by size and weight and you couldn't care less about the words themselves.
For purposes of selling, its common to classify books by genre because people DO routinely say, "I'd like to read a mystery story today" or "I'm looking for a romance." People rarely say, "I want a book by a left-handed author with blonde hair", so we don't normally classify books that way.