It seems every once in a while a game will come out where ReShade will cause the game to not process any keyboard inputs. In this case, none of the keyboard keys work in the menu and ingame. The mouse works in the menus, but ingame the mouse cursor will leave the edges of the screen if you turn far enough (I'm on Fullscreen).
I'm on the 3.0.8 ReShade version.
Here's the log on pastebin
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Edit:
Disabling the Origin overlay made it work. But obviously can't invite friends now or accept party invites.