Should mutually exclusive be removed from the English language?

No

Why do you ask? Do you think mutually exclusive is redundant, like mutually agree? Or do you think the word mutually is misused in that phrase?

The word mutual implies reciprocity. If two people have mutual hatred, they hate each other. (Some people use mutual to mean shared in common, as in our mutual friend. Not all linguists agree on that usage, however.)

It is redundant to say two people have mutual hatred for each other. The last three words are superfluous. They have mutual hatred and Their hatred is mutual are adequate, as is They have hatred for each other and They hate each other.

So what about mutual exclusivity or mutually exclusive? If the the exclusion is reciprocal, then the term is okay. If two things are mutually exclusive, they can't exist together; they exclude each other; the existence of one precludes the existence of the other. That implies reciprocity. I don't have a problem with either term and think permanent banishment from the language is a bit extreme.

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