This is a simple patch that allows the soaps and wash waters from Keep It Clean to clean off the dirt/blood from Dirt and Blood. The default version will clean off the dirt from both mods, but only applies the "Recently washed" clean status from Dirt and Blood instead of the clean buffs from Keep It Clean. It is intended to be used with the "Start Keep It Clean" checkbox unchecked, as that appears to only disable the Keep It Clean dirtiness tracking, which allows you to use the Dirt and Blood dirtiness system with the bathrooms and soaps from Keep It Clean. To prevent doubled up buffs from Keep It Clean turning itself on, you will also want to get this script replacer mod here: https://www.nexusmods.com/skyrimspecialedition/mods/47095.

If you would like to use both dirtiness systems at the same time, there is an alternative version that includes a script edit which applies the Dirt and Blood "Recently washed" status every time the Keep It Clean clean statuses are applied. This should be equivalent to what you would have if you are currently using both mods and bathing twice to get clean. 

Note that I did not set up the Keep It Clean soaps to "count" as a soap for Dirt and Blood's Wash and Rinse ability; if you have soaps required for Wash and Rinse these soaps will not be recognized. Instead, you should use the soap item directly. While it is doable to set up Wash and Rinse to recognize the Keep it Clean soaps, it removes the soap from your inventory without applying the soap's special buff, which seems like a waste of a fancy soap. If you would like that ability and do not want to add them to the  "dirty-listofsoaps" formlist yourself, though, let me know and I can upload a version with that included.