The key incompatibility comes with the fall. How God created the earth and the animals in it is of little consequence, other than in confirming the Biblical testimony. I have no problem with God speaking the world into existence and on the day of creation that world having sedimentary rocks, canyons, rivers, and full grown trees that would have visible rings if you cut them down.
The incompatibility is the fall. If Adam and Eve had not sinned and separated us from God; then Jesus need not have come. If mankind evolved simultaneously in various locations, that is a major theological problem. In order for the gospel to be true we have to be able to trace mankind back to a single man and woman.
That should be the focus of the argument.