I think there may be some confusion about "poopy butt." Two things come out of a rabbit's rectum. (1) One is poop, which normally consists of round relatively dry small pellets. For a healthy rabbit, these relatively dry pellets do not have a fecal smell or odor. They have a herbal smell with a onion or slightly sulfur overtone. (2) Two is a cecum pellet. A cecum pellet exits the rectum about once per day. It is soft and gooey and if you smooch it in your fingers, it has a vomitous smell. I do not regard it as being poop and your rabbit also does not regard it as being poop either. Rabbits, like cows, goats, etc, have a stomach that serves as a digestive brewry to convert cellulose to glucose. Cows, goats, etc, regurgitate the contents of their cellulose brewry stomach to their mouth to rechew, and re swallow. For a rabbit the cellulose brewry stomach is located at the juncture of the small intestine and large intestine...it's called the cecum. It's their major stomach. (In humans it's called the appendix) To dump the cecum, for rechewing, they cannot regurgitate the contents because of the cecum's location. The cecum's contents have to exit through the large intestine and out of the rectum. When a rabbit senses that it's going to poop, it runs to its litter box. When a rabbit is going to pass a cecum pellet, it does not regard it as poop, and will immediately bend over and eat the pellet. You can, like me, have a pet house rabbit for years and never know they are passing a cecum pellet every day! My two 6 months old Flemish white babies have absolutely clean butts because they eat their cecum pellets immediately. What can happen, is that with age, if your bunny becomes fat or develops spinal autheritis that makes it painful to bend over, the cecum pellets will be passed to drop on the floor/carpet or to clog up in the fur around their rectum. This situation existed with Bunny for over a year. We thought it was an incident of aging. Her cecum pellets, when stepped on, seriously stained out bedroom carpet. I also had to hold her in my lap upside down and clean her butt with damp tissues. Ultimately, I noticed she was becoming not very active, just laying in the floor. Then I noticed her licking her front paws excessively...I knew that was a sign of an animal in pain. I took her to the vet, and ultimately an X-ray revealed spinal stenosis. Flexing her spine was painful. The vet prescribed Metacam, an anelgesic, and she became a new active bunny! Very mobile and once again started eating her cecum pellets...NO MORE DIRTY BUTT, no more stains on the carpet.
The above is my anecdote. If you bunny has a dirty butt, certainly what I described above could be a cause. It's also possible your bunny has diaherrea so that it's normally dry poop is coming out runny. So therfore, it's possible this gooey stuff could really be poop.
The cecum pellet is a gelatinous mass of highly concentrated bacteria (that converts cellulose to glucose), pieces of cellulose that have been difficult to digest, finely chewed up vegetation, and liver enzymes. The enzymes give the pellet it's vomit like bad smell. It looks black, but if your bunny has been eating dark green vegetables, it will have a dark green color if you smooch it out and look at it. This dark green color can really stain your carpet! For a human being, the cecum pellet is not bacterially dirty. The cellulose to glucose converting bacteria in the cecum pellet is completely harmless to a human. By the way cellulose is a polysaccaride... a long hydrocarbon chain, If you cut it it off into small pieces at the right places, you create glucose molecules. The symbiotic bacteria in the cecum stomach are fed by this glucose they make from cellulose. Since they make more glucose than they need, the excess glucose feeds your bunny. Such a good deal for the bacteria and the bunny!