These have been addressed in microsoft#1232. Note this does not imply compatibility with repositories with multiple files whose names differ only in case -- that is a separate (and quite larger) item.

Unfortunately, certain basic operations fail on Linux with the existing code, e.g. (assuming master contains foo.txt):

git checkout -b foo
git mv foo.txt Foo.txt
git add .
git commit -m foo
git checkout master

leaves both foo.txt and Foo.txt in the working directory; the latter should obviously have been deleted by the second checkout.

This is due to case-insensitivity in the modified paths database and virtualization code, among other things, which results in case-differing-only filenames being dropped from the data sent back from the GVFS provider, via the virtual-filesystem hook, to git itself after it reads its index file.

Therefore, we will almost certainly need to ensure these internal data stores in the GVFS provider are case-sensitive when running on Linux. Doing so (e.g., with the the WIP in 4fd47be) appears to resolve the failure of the GitCommandsTests.CaseOnlyRenameFileAndChangeBranches() functional test, which performs the git steps shown above.