Why do you want to run firefox in the background?

Daemons are system service that are ran in the background servicing the system or waiting requests from other apps. Firefox is a user app that the current user interacts with. It is not considered a daemon so it won't run in the background unless you execute it and minimize it to be used later. Again, it is meant for user access not system service.

When an application such as firefox is launched in a GUI the cli output is hidden because it is in a non-visible shell which is basically in the background. Now if you meant that the application would be launched like a daemon process and will always be running then that can be a mistake, many applications (most notably web browsers) do have memory leaks which cause them to keep consuming memory/RAM and even increase their memory use when not being used, you should only run the application you need at the time and to avoid this memory hole and potential vulnerabilities from the running applications.