If animation is set to move, when hud automatically hides, every GUIs including which from EssentialGUI and vanilla are moved down a certain distance visually, while the actual position where you can click them remains the same.

https://www.curseforge.com/minecraft/mc-mods/essentialgui

Wait this mod is not opensource... should I stop using it then

EssentialGUI changes a lot about the UI, and since (as you noticed) it's not open source, I have not looked into adding compatibility at all yet.

While I think EssentialGUI is antithetical to AutoHUD, I have fixed the whole UI being shifted in AutoHUD 2.2.

I have only tested the standard, basic configuration of EssentialGUI. Feel free to reopen if there's problems with specific setting combinations of either mods.