If you modify the Global Mapping at Prefs > Mapping > Global Mapping, like f.ex. map the Menu button (or its hold state) to launch Plex, this will - as is being warned right there - hardwire the respective button to that action and make it unavailable to other applications.

For apps like Plex, this also means that the "Open Remote Buddy menu" action - which is by default mapped to "Menu (held)" - will automatically be relocated to another button code, which can trigger more automatic rearrangements of actions, which in turn can lead to the result you describe. The purpose of this is to ensure that you don't lock yourself out of access to Remote Buddy's menu. If you really, really want to lock yourself out of Remote Buddy's menu, you can, of course manually adjust the Plex Behaviour mapping at Prefs > Mapping > Plex to achieve just that.

For the Apple Remote, it's best to leave the Global Mapping table at its defaults. It just has too few buttons as that you could afford dedicating one to exclusively execute a single action. That'd also limit or end your ability to correctly control applications like Plex, which require the use of all buttons for navigation.

If what you really want is to launch Plex with a press of the Menu button when no other controllable software is currently active, the right place to make that change is at Prefs > Behaviour > Default Behaviour. The Default Behaviour is used when no controllable application is active.

Hope that helps.

Best regards, 
Felix Schwarz