The README says to turn on localhost support in Chrome, but this option doesn't exist in the Firefox version of the extension.
Firefox Developer Edition 62.0b13 (64-bit) on macOS 10.13.6
What README are you talking about? I'm not sure what this issue is referring to or what "can't run in localhost"
In the FAQ, it says "If you are running your app from a local file:// URL, don't forget to check "Allow access to file URLs" on the Chrome Extensions settings page. You can find it by opening Settings > Extensions." The extension also does not detect my app when running in localhost, but there is no "Allow access to file URLs" option in the FF version of the extension.
Ah, I see. localhost and file URLs aren't the same thing. Localhost refers to "http://localhost" and file URLs refer to e.g. "file:///some/file/system/path"
You should not need to select any special setting for DevTools to work with localhost URLs
Hmmm, it's still not working for me on FF dev 62.0b13.
Can you elaborate on what you mean by "not working"? Does the DevTools extension show up? Does it say anything? Are there any errors in your console?
I get this message. No console errors.

Is your application running in a <frame> or <iframe>?
Nope. The DevTools console panel does work, however.
I thought you said DevTools wasn't working? So it's just the little icon up top that detects which version of React is running?
Yes, that's right:

Abstracting this up a level, I would like to "softly" suggest this might be an issue with FF, every react site seems to "[Not appear to be using react]" when I attempt to use React Dev Tools to inspect.
Confirmed in 63 Nightly and 62 DevEdition.
Issue was identified as a regression in Firefox. It is being fixed and requested to be uplifted to 62. Tracking in bug 1483684.
Stay tuned and pardon the dust 👷
Aug 16 Update: Nightly 63 fixed.
Aug 19 Update: Uplifted to beta. Next build, 19, rolls out Aug 21.
Did it?
Where can I configure the FF extension to "Allow access file URLs"?
React DevTools has been rewritten and recently launched a new version 4 UI. The source code for this rewrite was done in a separate repository and now lives in the main React repo (github.com/facebook/react).
Because version 4 was a total rewrite, and all issues in this repository are related to the old version 3 of the extension, I am closing all issues in this repository. If you can still reproduce this issue, or believe this feature request is still relevant, please open a new issue in the React repo: https://github.com/facebook/react/issues/new?labels=Component:%20Developer%20Tools
Most helpful comment
React DevTools has been rewritten and recently launched a new version 4 UI. The source code for this rewrite was done in a separate repository and now lives in the main React repo (github.com/facebook/react).
Because version 4 was a total rewrite, and all issues in this repository are related to the old version 3 of the extension, I am closing all issues in this repository. If you can still reproduce this issue, or believe this feature request is still relevant, please open a new issue in the React repo: https://github.com/facebook/react/issues/new?labels=Component:%20Developer%20Tools