You can grant friends access to your computer with permissions set specifically to just the controller, the mouse, the keyboard or some combination of the three. When people are connected, you can assign the permissions in the bottom-left in Parsec by clicking their profile picture.
Keep in mind that this is only a thing when you're hosting using the Computers tab. Arcade does not have any permission settings, and guests in Arcade can only use a controller, or use their keyboard as if it were a controller.
Tweaking default permissions
By default, anyone connecting to you will only have controller permissions. Although, note that if you connect to yourself with the same Parsec account as the host computer, you'll start with all permissions by default. To tweak what permissions your friends will get when they join you in the Computers tab, you can use the Friends icon in the left, click a friend, and give the permissions you want.