Make it an extension API.
The GP noted that the more concerning thing going away isn't Firefox presentation of feeds (the live bookmarks) bit the discovery. So far, you can use the orange button to learn which page supports RSS or even learn that RSS exist in general. Without that button, even if there are extensions, only people who already know what RSS is will be motivated to install them.
Now we get that kind of default discoverability instead for proprietary services like Pocket...
A low-maintenance compromise would be to keep the button, but make it strictly extension-only. Provide an API/manifest entry where an extension can register as RSS reader. If the button is clicked, that extension gets a callback. If no extension is installed, open the Browse Extensions tab and offer an option to hide the button.
The Firefox devs would still need to maintain the button and feed discovery logic (which mostly checks for a specific meta tag, I think) but could still throw out live bookmarks, the Atom parser, etc.