The problem doesn’t have anything to do with GSX, it’s the simulator own menu that is stuck, it’s a known P3D bug that happens only with 5.1 and only when using the new Html menu system.
What’s really happening here, is another application calls the Simconnect menu, but instead of displaying what it’s supposed to display, it will show entries from a previous application the called the menu system, or it's just stuck.
You said Active Sky menu or the ATC menu doesn’t work, it’s likely one of these is showing the GSX menu instead, it’s not GSX that called it, it’s just the menu stuck with the last set of entries.
Since GSX pushback is usually the last menu you call before takeoff, I can see how easily one can be mislead this is a GSX issue, but it’s not, it’s just the simulator own menu that is stuck.
The most telling proof of this, is that is not fixed by restarting GSX (if it really was a GSX problem, it would, since GSX has no memory of a previous session between restarts), and it’s only fixed by restarting the sim.
Many users reported this is fixed by reverting to the previous Scaleform based menu, as explained here:
https://www.prepar3d.com/forum/viewtopic.php?p=235715#p235715
