The phrase "fundamental incompatibility" refers to a situation where two things or ideas cannot work together or coexist because they are fundamentally different or incompatible with each other. Full definition
Species have come and gone throughout biological history, through chance, calamity, and — in the human - dominated world — through purposeful slaughter or, as in the case of the Yangtze River dolphin, fundamental incompatibility between us and another life form. (dotearth.blogs.nytimes.com)
The passage in James begins with an assertion of the fundamental incompatibility of faith in Christ, the Lord of Glory, with partiality in human relations. (religion-online.org)
Still, the principal difficulty in the way of UN adoption of the Charter remains, a fundamental incompatibility in the general outlooks of the two sides. (firstthings.com)