MogHunter’s MenuBackground, VisuMZ CoreEngine’s backgrounds* and SumRndmDde’s Menu Backgrounds are all unaffected by this plugin, as they use different mechanisms to load and display the menu background(s).
* as far as I can tell. The VisuMZ series of plugins is obfuscated, which is why I generally don’t add specific compatibility tweaks for them and don’t guarantee any level of compatibility with them in particular.
Your best bet would be to see if you can implement the background changes with one of those plugins alone, or alternatively to write a small plugin that displays a Picture sprite in the background of menus.
It may also be possible to use my Live Menu and Pause plugin to get the desired effect (as it can keep the map scene active without filter), but this would require at least some Event scripting to show/hide the background and may not always be perfectly in sync.