Two nits for the price of one:

On a *nix filesystem I want to open either File or FILE or throw an error if they both exist.

Do you really want to "throw an error" or do you mean "be alerted to the existence of two files with similar names?" The names may be similar, but the content need not be identical. (And -- not a nit; just curiousity: do you care about whether the two are in the same path?)

On Windows and Darwin this fails, as both files always exist, but are the same file.

At least on 'doze, IMO that's a misleading statement:

Only ONE such file exists, but because w32 is case-insensitive-but-case-preserving any attempt to create "FILE" in a particular \path\to\dir\ which already contains "File" will (for some aps) produce a (windows-rooted) warning "File already exists; overwrite?" or (windows-native) error message that "Duplicate name exists...".

Sidebar: At least some aps which automaticly create/overwrite a .bak file on save, will create (in the example above) the .bak as "FILE.bak" (case transformed to match the new name).