Is there a way to make Firefox use Mac's native fullscreen when watching a video (e.g. on Netflix)? The browser does go fullscreen, but it's not on it's own space on macOS.
I'm currently using Firefox 57 and macOS 10.13.1.
Unfortunately, that's not currently implemented in Firefox (see Bug 1403085).
As a workaround, consider putting Firefox itself into fullscreen mode by clicking the green button in the title bar before making a video fullscreen.
Usually video players will have a full screen option you can toggle on/off.
Using your example of Netflix, you'll see this option at bottom right when you hover your mouse over the bottom of the video.
In the screenshot above, the icon at bottom left (immediately below the time remaining) is the full screen icon. Clicking on this will display the video in full screen.
To use a non-Netflix example, the screenshot below is taken of a YouTube video:
Likewise, at bottom left there is an icon for viewing the video in Full Screen mode. When you click on this icon, you'll see a prompt appear at top like the one below:
A similar prompt appears whether it's YouTube, Netflix, etc when playing videos in full screen mode.
Finally, to exit Full Screen mode you can just click the icon in the same location at bottom right (or just press the esc key).
This behaviour (i.e. icons, prompts, esc key) is independent of the browser. This will work in Firefox, Safari, etc.