Wild rabbits generally avoid heavy downfalls of rain, but, if they live in a particularly wet climate, like here in Ireland where your guaranteed rain almost daily, there’s no way they’d avoid it completely. The difference is, as bam said, that they aren’t being submerged in water. Their coats aren’t getting saturated. Like if you got caught in the rain, your hair (unless it’s very short or fine) will not get soaked to the roots unless it’s heavy rain or you’ve been out for hours, the top layer of loose hair may get wet, but your whole head wouldn’t.
So let’s say your rabbit was out wandering in the garden and your sprinklers came on, or it suddenly started raining, your rabbit will seek shelter. So unless your rabbit managed to get soaked through, you’ll likely find that if you run a cloth or even just a tissue over their fur, that their skin wouldn’t actually be wet. Fur is an amazing thing!