B737 MAX 8 Captain reported a ground conflict with inbound aircraft during gate pushback. Captain added that tug driver communication was nonstandard and that wing walkers were not wearing headsets.

Narrative

Several things led to this event. First someone installed a tail stand on a MAX; which after boarding the aircraft; the Ground Crew had difficulty removing. Tail stands are not used on MAX aircraft. Ground Crew was so preoccupied with that issue; they failed to realize they didn't have an operating headset set at Gate XX. A Ramp Agent brought over a headset case.During the push I happened to notice a company MAX 8 pulling into adjacent Gate XY; and that our nose had drifted left of the J-line. Basically towards Gate XY. I watched the wingtips pass by one another what looked like two feet. So unbelievably close. Wing Walker on Captain's side was not wearing a Bluetooth headset. Not sure if he was capable of relaying information to Tug Driver. I commented to Tug Driver about how close that the wingtips were. She didn't respond. I commented again about it. No response. I asked if she could hear me talking. She finally responded with; 'Sorry; I'm trying to settle my nerves.' I assumed because of how close we came to clipping wingtips. During the disconnect I saw that neither Wing Walker had headsets on. Only the Tug Driver.Ground Crews need to know how to do their jobs. This Crew used a tail stand on a MAX. Didn't have proper communication gear ready for the push. Any time two aircraft are on a potential collision course; perhaps they should be instructed to stop the aircraft immediately.