Is the Boeing 737 MAX 8 MCAS exceptional in operating when autopilot is off?
Are there other automated systems providing direct control surface actuator inputs when autopilot is off on the Boeing 737s?

One such system on the 737 Classic and NG is the Speed Trim System:



As you can see above, when certain conditions are met, of which 5 seconds has passed since a pilot trim input is made, the STS trims the plane if required.

The system's classification would be stability augmentation system. When light, rear loaded, and with plenty of power (during the climb phase of the takeoff or during a go-around), the 737 has a tendency to pitch (nose) up (since the engines are below the wing and below the center of mass); the STS would limit that.