two people who are incompatible have such different characters, beliefs etc that they cannot have a friendly relationship [≠ compatible]:
I don't know why they ever got married. They're totally incompatible.
two things that are incompatible cannot exist or be accepted together
Business interests are incompatible with public office.
Politeness and truth are often mutually incompatible.
two things that are incompatible are of different types and so cannot be used together [≠ compatible]
The laser printer is incompatible with the new computer.
incompatible blood groups
—incompatibility noun [uncountable]