B737 Captain reported ground personnel signaled the flight to park even though the auto park system indicated 'wait.' As aircraft approached gate; a baggage cart drove under the wing requiring crew to stop.

Narrative

Upon arrival to Gate XX at ZZZ; we were met by the standard ground team (Guide man and two Wing Walkers) situated on the XX parking line; however; the auto park system was also on and indicating 'Wait'. The Guide man gave us guidance to proceed; but given the conflicting guidance from the auto park system we held our position. While the FO was contacting station ops; I flashed the taxi light to signal our concern. The guide man turned around and noticed the auto park system's indication. He then continued to give us guidance to continue. We held our position. Station ops acknowledged our concern. Meanwhile traffic in the alley began to back up. The guide man feigned an attempt to reset or turn off the system but the 'Wait' indication remained illuminated. After enduring this impasse for several minutes; the FO and I reluctantly agreed to proceed only after sufficiently visually clearing the parking area. I signaled the guide man and we cautiously proceeded. Not a second later; a baggage cart proceeded into the area on the right wing. We immediately stopped and at the same time the guide man seemed to notice the conflict and re-actively changed his guidance to stop. After the obstruction on the right wing was clear we proceeded to park without incident. After parking; the FO and I debriefed. Then I sternly debriefed station ops and the guide man.