The rabbits here are English angora and we always breed right after they've had their wool harvested. They get such a heavy dense coat on them that if they weren't trimmed the mating couldn't occur.
Here's Sydney (the agouti) and Suzie (the REW) before their haircuts:
Here's the same two bunnies after their haircuts:
With a full angora coat, sometimes it's best to trim both the prospective new parents before letting them meet up with each other.