A bath won't kill them as long as they don't get chilled.
I use a bucket of appropriate size for the bunny and just lower the butt into tepid water... just at body temperature. Once the hind feet are on bottom, they usually don't struggle much. Just swish the poop off, remove bunny, dry on an old towel and place the bunny out of drafts until he is thoroughly dry.
If your temperatures are chilly (below 70 degrees) they may need a bit of added heat. A hot water bottle (can just be a screw cap wine bottle inside a sock) could be provided.
Edited to add: Giving the bunnies certain greens will firm up their stools. The lawn weeds Plantain and Shepherd's Purse are excellent, as are the leaves of raspberry, blackberry and strawberry.
I use a warm wash cloth and if I need to ,a little soap, and just wash the poopy part,[no need to get the whole rabbit wet] - rinse well with clean warm water, then I dry them with a hair dryer [don't burn them]
If this is an ongoing problem rather than a passing upset, it could be a sign on weaning enteritis, which is potentially fatal. Removing the pellets entirely and feeding grass hay and kitchen oatmeal (like Quaker Old Fashioned/Large Flake) is the usual treatment. The plants I mentioned previously should help a lot. You can add the pellets back gradually once the rabbits are back to normal.
The doe should be okay just on hay and oats for a few days, but you may want to feed her pellets away from the youngsters. Either put the doe in another cage for a couple of hours so she can eat pellets or remove the kits while she eats pellets, whichever is easier.
How are they doing? Any more poopy butt or has it settled down?
One litter is resolved. Out of the other litter, I cleaned 2 butts yesterday in the morning and 4 butts when I got home. This morning I am cleaning zero butts so I hope this is a good sign! All kits are happy and very playful this am. Fingers crossed!