It is odd that he prefers to drink in that manner. As Wick says, constantly wet skin is a prefect breeding ground for bacteria and other microorganisms. The skin loses its proper barrier capacities due to the wetness and in short, it’s not good at all.
I think I’d trim back the clumped hair just a little bit, taking great care not to hurt the skin. Then I’d put on a fat barrier cream for protection and try to teach him to drink from a bottle. Sometimes that can be achieved by smearing some banana onto the bottle nozzle.
You must keep track of the amount he drinks though, so he doesn’t get too little water in him. Too little water can lead to constipation. Some amount of water can be provided by serving his greens dripping wet.
If this doesn’t clear up soon you should see a vet about it. Try to keep a very close eye too see so it’s not caused by drooling rather than the way he drinks, as Wick suggests. Teeth problems are very common in rabbits.