Locally it shouldn't. xdotool is used to simulate keyboard input and mouse activity on X11 systems, so it requires those perms only if you're running it over a network protocol like VNC.
I use Debian, but if I recall, using and configuring a VNC server like vinagre should fix this. Hope this helps.
@UncleIroh That's what's weird; It's all local. It also only grants permissions for a single xdotool command, then it loses them and will not reprompt you unless you kill the remote permission notification. Goofyness abounds.