Abs comes on when turning at slow speeds when parking 2003 sierra

Most likely you have a wheel sensor going out. The only way to tell which one is with a data scanner that can access the ABS system.

It will see all the tires spinning at the same speed until one shows a different speed.

Also make sure you have all the same tires and the air pressures are the same.

Here is a copy of a GM bulletin that applies to you concerns of low speed ABS activation.

Antilock Brake (ABS) Activation At Low Speeds (Clean Wheel Speed Sensor Mounting Surface) #03-05-25-007 - (09/29/2003)
Antilock Brake (ABS) Activation At Low Speeds (Clean Wheel Speed Sensor Mounting Surface)

1999-2004 GMC Sierra

Condition:
Some customers may comment on ABS activation at low speeds, usually below 8 km/h (5 mph). Upon investigation, the technician will find no DTCs set.

Cause
The cause of this condition may be an increased air gap between the wheel speed sensor and the hub reluctor ring due to rust and debris built up on the sensor mounting surface.

Correction
Measure AC voltage and clean the wheel speed sensor mounting surfaces.

Raise and support the vehicle.
Disconnect both the front wheel speed sensor (WSS) connectors at the frame and harness.
Place a Digital Volt Meter (DVM) across the terminals of each WSS connector.
Rotate the wheel clockwise approximately one revolution per second. The minimum reading should be at least 350 ACmV's. If the reading is less than 350 ACmV's, remove the wheel speed sensor. Refer to the applicable Wheel Speed Sensor Replacement procedure in the ABS sub-section of the Service Manual. Plug the WSS bore in order to prevent debris from falling into the hub during service.
Clean the WSS mounting surface on the hub to remove any rust or corrosion using a wire brush, or equivalent.

Important
Make sure that the sensor sits flat on the hub. Check the sensor flange against a straight edge to ensure flatness. If the sensor flange is distorted, replace the sensor.

Apply a thin layer of bearing grease to the hub surface and sensor O-ring prior to sensor installation. Use ONLY Wheel Bearing Lubricant, P/N 01051344.
Install either the original sensor or a new one in the hub. Ensure that the sensor is seated flush against the hub. Refer to the applicable Wheel Speed Sensor Replacement procedure in the ABS sub-section of the Service Manual.
Place the DVM across the sensor terminals and recheck the voltage while rotating the wheel. The voltage should now read at least 350 ACmV's.

Good luck and thank you for using Fixya.

There is a small sensor on each rotor and spindle. If the sensor is jammed full of **** or debris it wont get a good signal.