Your best solution is to solve the problem of the poopy butt, which is most commonly diet related. Correct the diet, correct the problem and no more poopy bum. In the meantime you could very carefully trim some of the fur around where it is sticking, and on any bare skin such as the testicles where it is sticking, applying a very light coating of petroleum jelly may help prevent it sticking on there. But you really need to work at correcting the problem so it doesn't develop into much worse health issues such as enteritis, bloat, and fly strike.
If he is producing normal round fecal balls, then it will be the cecotropes that are sticking and causing the problem. Normally cecotropes will be immediately reingested by the rabbit from the anus, but certain health issues can cause this not to happen. If the cecotropes are not fully formed into blackberry clusters, and are mushy or pasty at all, this is caused by a microbial imbalance in the rabbits cecum leading to the improperly formed cecals. This is called cecal dysbiosis. Medications, stress, new foods can sometimes be a cause of this, but most often it will be because of too many carbohydrates in a rabbits diet, from treats and/or pellets. The best way to correct this is to free feed a good quality grass hay like timothy and cut everything else out of the diet temporarily. When doing this, it's best if the rabbit is already a good hay eater as you have to ensure they are eating plenty of hay to make up for the lack of pellets or they could starve themselves. You also have to keep a close eye out for any decline in activity or eating/drinking, and any change of behavior, and also monitor the rabbits weight in case there are is any unwanted weight loss. If any of this happens then there could be a more serious health problem causing the poop problem and you will need to get your rabbit to a rabbit savvy vet right away.
Once on a hay only diet, usually within a week or two there will be signs of improvement, though in more severe cases it can take longer. Once the poopy butt clears up for at least a couple weeks, then other foods can gradually be added back in, one at a time and starting with small amounts, though usually you can't feed the same amount of pellets as before or the poopy butt will come back, unless the poopy butt is being caused by other foods such as too many sugary treats, or in rare cases a sensitivity to certain veggies.
If the cecals aren't mushy but are fully formed and just not being reingested, things like stress, too rich of a diet, environmental distractions, dental problems, obesity, and arthritis can be some possible causes.
The best thing is to consult with a rabbit savvy vet regarding the problem and how to go about correcting it, including any dietary changes. But when I start seeing poopy butt, this is usually how I go about trying to correct it.
http://sawneeanimalclinic.com/downloads/chronic_intermittent_diarrhea_in_rabbits.pdf
http://rabbit.org/intermittent-soft-cecotropes-in-rabbits/
http://rabbit.org/disorders-of-the-cecum/