Q: 2017 mercedes e300 with 17K miles shakes while idling with AC on. Why?

This is normal when the AC is on. The air conditioning compressor requires torque from the belt system on the engine to power it. When the AC is off, the compressor clutch does not activate, meaning the AC is not straining the engine. When the AC is on, the compressor clutch activates, wherein the drive belt on the engine now turns the compressor which in turn is compressing refrigerant so you can be nice and cold. The Idle Control Actuator is what controls the engine idle. When the AC kicks in, the engine will drop some RPM, and the actuator opens to allow more air into the engine. When you are at speed, the throttle is open from the accelerator pedal under your foot. the Idle control actuator is not active at this time. I would suggest having an exert from YourMechanic come to your location to take a look at the vehicle to verify what may be causing the rough idle.