I have tried every variant when it comes to whitelisted media types and uploading WebM doesn't work. At one point -- many weeks ago -- it worked. This was before the introduction of Accepted Media Types setting, I believe.
In my File Upload settings for Accepted Media Types I've currently got this: image/*,audio/*,application/*,video/*

When selecting a WebM file it brings up the dialogue but when you press "OK" to upload the file it gives the following message: The file type is not accepted.

Images, audio, PDFs and other files work fine. But not WebM.