The W3C Browser Extensions Community Groups has been working for a while on compatibility between browser extensions on different platforms (Chrome/Firefox/Edge/Opera/Etc.).
They have a list of keys which should be safe to use. An important one being browser_specific_settings so you can specify proprietary settings for different browsers without the manifest being marked as ill-formed.
I need to add an ID for my Firefox addon under this key, but Chrome is not supporting this out of the box and shows an error if the extension is installed - Is there a way to tell Chrome to ignore this key? (without scaring the user that the extension is broken when it isn't)
The answer was originally confirmed in a comment
No there isn't. And Google doesn't care about that coordinated effort like totally. You'll have to provide a separate build of your extension for Chrome. – wOxxOm