IDIOMS

oil and water

(idiomatic) Two things which are incapable of mixing or coexisting harmoniously with each other.

Example: 1982, Winston Graham, The Miller's Dance, Pan Books (2008), ISBN 9780330524230, unnumbered page:
  We are oil and water. There are few things he and I agree on but I believe we would agree on this.
2009, Brian Schofield, Selling Your Father's Bones: America's 140-Year War against the Nez Perce Tribe, Simon & Schuster (2009), ISBN 9781416539933, page 31:
  […] second, that the white and red man were oil and water, incapable of safely sharing a landscape.
2011, Loretta M. Siani, The Alchemy of Prayer: How It Began and Why It Is the Medium of Miracles, iUniverse (2011), ISBN 9781462003174, page 47:
  Forgiveness and making bargains are oil and water. They don't mix.
For more examples of usage of this term, see Citations:oil and water.