Cleanroom focus is on "correctness" - design must be correct.
OO focus is design quality: maintainable, reusable, etc.
 
These complement and do not contradict.

A key part of OO is partitioning to sub-specification (classes, inheritance, etc.) This is shared with Cleanroom.

In OO objects may be related through the use of inheritance. For Cleanroom Box Structures this allows creating a new data abstraction without having to simply copy an old one.

Polymorphism is difficult because it is difficult to know which method is being invoked. One way to deal with this is to have each possible method documented, another is to note at the abstract level they are identical even though their individual implementations are different.