The issue seems to stem exclusively from the AppData/Local/LastHope/Saved/Config/WindowsNoEditor/Input.ini file. If I completely delete the WindowsNoEditor folder (causing it to be recreated entirely), and replace the Input.ini file with my old save's Input.ini file, and modify nothing else, then launch the game, the issue is reproduced.
It can also be reproduced by launching an old version of the game (e.g. LastHopeV20.6) after having cleared the WindowsNoEditor folder, opening up the keybindings under options, and rebinding a key, causing the Input.ini file to be resaved.
Something of note is that I have bound my right-mouse-button to the walk forward input. I have noticed that the new "Tablet" option seems to force the user to have either the LMB/RMB selected (or, at least, I cannot figure out a way to avoid it from defaulting to one of the two). I suspect your issue may be rooted here.
As a side note, is that behaviour mandatory? I quite prefer using LMB/RMB for alternative options, and would rather bind the tablet to TAB (or alternative).
Last Hope that helps!