The expression “mutually exclusive” is used in statistics to refer to events that cannot occur at the same time. For example, with $10 in my pocket, I go into a store intending to buy a battery and a jump drive, but each item costs $10. I can buy the battery or I can buy the jump drive, but not both. The purchases are “mutually exclusive.”

Writers use the term when discussing subjects that seem to be so opposed in nature as to be incapable of coexisting but which, in their opinion, can in fact do so. For example:
Privacy and Security Are Not Mutually Exclusive.
Interpretation: Security, in the sense of government defenses that rely on surveillance and data gathering, is being contrasted with privacy, the condition of being free from public attention.

Are Religion and Science mutually exclusive?
Interpretation: Religion, which requires adherents to believe in events that defy the laws of physics, is contrasted with science, which insists on physical proofs before belief.

The Germans don’t see brains and brawn as mutually exclusive.
Interpretation: “All brawn and no brains” is an idiom that reflects the popular belief that athletic qualities and intelligence are not to be found in the same person. The statement posits the idea that intelligence can be expected of athletes.

Three other common expressions that use the adverb mutually to mean a reciprocal action or status are:

Mutually beneficial: good for both parties.
Example: After 1940, Mexico and the United States slowly crafted a mutually beneficial relationship.

Mutually delighted: good feelings on each side.
Example: By the end of their first term together, in the spring of 1874, it was clear that teacher and pupil were mutually delighted.

Mutually assured destruction: a state of hostility in which two equally strong opponents are capable of destroying one another in open conflict.
Example: Fifty years ago this week the idea of mutually assured nuclear destruction was outlined in a major speech. But how did this frightening concept of the Cold War fade from people’s psyches?