This article explains how to cast from Mozilla Firefox on Android to a Google Chromecast streaming device.
Cast Almost Any Web Video from Android to Chromecast or Fire TV [How-To]
There is currently no casting icon directly in the Firefox for Android app. However, you can opt for a third-party extension, such as the fx_cast extension, which adds a casting feature to Firefox. This option requires an app that supports XPI files and a bridge for a successful connection.
However, a workaround outside of the Firefox browser is to use a Chromecast built-in app, such as Netflix. Step-by-step instructions can be found in How to Chromecast Netflix.
Although Windows, macOS, and iOS support Firefox, these operating systems do not support the casting functionality.