HTML 5 video has many mechanisms to restrict media access based on client properties. For example, there is a robustness parameter which implementations are expected to evaluate according to their perceived ability to prevent user-controlled access to content.
I suspect that Widevine (the DRM plugin used by Firefox) did not provide a robustness level on Linux which Netflix was comfortable with. To a degree, this is still ongoing. I think the maximum resolution you can get on Linux still is 720p, while Windows will go to at 1080p at least.