What you describe sounds like sticky poop or poopy butt, aka cecal dysbiosis. It’s not a veterinary emergency. It’s often manageable with some tweaking of the bun’s diet. Rabbits should eat lots of hay, a smaller amount of pellets (2 tablespoons for a 2 kilo bun) plus a small helping of leafy greens. Some rabbits are prone though, and dietary treatment can need quite a bit of time before improvement is seen.
The least stressful method to clean off poopy butt is to massage corn- or potato starch into the sticky clumps, then brush or pick out the clumps. If that’s not an option, you can do a butt bath. You don’t need to bathe the whole bun, just the hind legs and the butt. Use lukewarm water in a (plastic) wash basin that you put on the bathroom floor (it should be near the floor in case the bun jumps out), place the bun so it can support itself with its forepaws on the rim of the wash basin. Gently rinse out the clumpy poop using one of your hands.
In more severe cases you might have to use a small amount of soap (preferably perfume free), but in most cases, lukewarm water will be enough. When the poop is washed out, dry the bunny butt with a towel, I prefer a microfibre towel. In winter you can use a hair dryer on a low setting, a wet bun gets cold if the ambient temperature is on the lower side. Many buns find this so soothing they’ll fall asleep while they’re being dried!
Here’s some trusted info on Intermittent Soft Cecotropes in rabbits: Intermittent Soft Cecotropes in Rabbits | House Rabbit Society