You can either turn off the plugin that changes the logout menu in RuneLite, or click the toggle button to turn off login screen detection altogether.
I'm not familiar with that plugin I'm afraid, but all the login screen detection is looking for is a small block of black pixels halfway down the left side of the screen. You'll be able to tell if it works on your setup by just running the server script (no need to connect your phone) and sitting on the login screen for 10 seconds until it does the check. The text on the server app should turn red and let you know it's seeing the right thing.