You are not adding a manual exception to keep that specific site with its partitioned cookies, you are instead keeping the cookies for that site and removing the partitioning they have.
For example, if I add an exception for youtube.com, I should only be logged in on youtube.com. But currently, since it is broken, your cookie is not partitioned and every site with an embedded YouTube video can access it. So depending on where you add an exception, it can be pretty bad.