Currently if you have a stack of pristine rags that are disinfected, if you split (right click) the stack, both the original stack of rags and the newly created stack of rags will both have the disinfected status. If the original stack of rags is worn/damaged/badly damaged and disinfected, if you split the rags, the original stack will be disinfected but the newly created stack will lose the disinfected status.

So:
Stack of pristine disinfected rags -> Split -> two half stacks of disinfected pristine disinfected rags

Stack of worn/damaged/badly damaged disinfected rags -> Split -> one half stack of worn/damaged/badly damaged disinfected rags and one half stack of worn/damaged/badly damaged rags (not disinfected)