As for books, try donating them to a library first, especially if they’re important books like old altar Missals or Roman Ritual, something of historic or academic importance. Secular libraries probably won’t want them but Catholic college libraries might have a place for them even if they need re-binding or other repairs.
If they’re just paperbacks and truly need to be disposed, it’s true that the old recommendation was to burn them. There are many people today who think it’s more responsible to put them into the recycling system. Personally, I think it’s equally respectful because either way the text is still destroyed rather than simply allowed to rot away or be put in with other truly dirty trash. Recycling is truly better for the environment and we should take that into account.
Decades ago, everyone had a fireplace or a wood stove, so burning things was rather easy. Today, not so easy for many reasons.
When vestments were made of natural fibers (cotton, linen, silk etc) they were biodegradable and burned easily or just returned to the earth if buried. Today’s synthetic fibers don’t act that way, and if burned will often just turn into a big lump of messy plastic (not good if someone does have a wood burning stove). Bury a polyester vestment today and it will still be there 500 years from now.
Once a thing is disassembled so that it’s no longer what-it-was as a whole, it ceases to be blessed. Vestments can be cut into strips. They don’t have to be tiny strips, just enough that they’re not vestments anymore. Cut the crosses and any Christian symbols.
My current parish, when I first arrived, was full of old polyester and felt vestments from the 70s. We made light work of them by just cutting them into a few strips then putting the strips into the trash can.
Some Missions like to get old vestments. Some do not. I had a mission parish a few years ago and the last thing I wanted was old vestments—I kept having to turn them away (same for old cheap chalices). If you know of a mission that truly asks for them, by all means send them IF (only if) they’re dignified and usable. If they look like rags, and you wouldn’t wear it yourself, why think a mission priest would wear it?
I like the idea of the Mission Society that takes vestments and uses the cloth for crafts. I think that’s great that someone can get joy from a recycled vestment part.