Mutually exclusive and not mutually exclusive [closed]

As Drew says in his comment:

"not mutually exclusive" is correct English and meaningful. It means that the two or more things concerned are not mutually exclusive: they can overlap.

However, I suspect you misunderstand the caution against "double negatives". This caution revolves around words that are or contain variations of "no" and "not". For example:

I didn't go nowhere.

They didn't never agree.

The problem is that, in certain English dialects, the duplication of "no"/"not" is used as an intensifier, despite the logic of the sentence being the opposite of what is intended.

When you use "no"/"not" with a different word that happens to have a negative meaning, it is universally clear what you mean.