It is customary to cut angora rabbits’ fur very short 3-4 times per year. It’s called harvesting, but angora rabbits actually wont be at all happy unless you harvest their fur regularly.
My teddy lionhead was shaved when he came to me. It was after the unseasonably hot summer of 2018, so his former owners had shaved him so he wouldn’t get so hot. It wasn’t a close shave, rather sth like 2 cm (about an inch) above the skin, except on his head and face. (I always cut away the fur around his eyes so he can see properly).
If a rabbit or dog is prone to forming fur knots, (some individuals are and some are not), it’s good to cut back the hair. You can cut vertically (perpendicularly) into the knots that are close to the skin, so you can part them manually and pluck out “dead” fur. Then, if you maintain a regular brushing routine, chances are you can keep the fur knot-free.
Rabbits don’t have continuous hair growth like we do, so how long it takes before the fur grows back will depend on where in the fur growth cycle your rabbit is when you shave/cut his fur.