I have reviewed the Fancy Menu Incompatibility issues, and they mention a simple fix for the mod menu button not being moveable, etc. However, there is no reference about a "Freeze Screen" issue.

The frozen screen issue happens on the Title Screen, and ESC menu screen where the Mod Menu button is available. No crash, so no code to share. I have to kill the java funtion to close the game. I have downloaded all recent versions of the mods for v1.20.1.

I understand this is not a sole Mod Menu issue, but since Fancy Menu is quite popular with modpack developers, it would be nice if the two mod developers could collaborate and find a solution.