B737-800 Captain reported a conflict with an aircraft being moved under tow too close to the reporter's aircraft.

Narrative

We landed on Runway XX and we were cleared to Gate XX by Ground Control. Approaching our gate we noticed that it was occupied by a CRJ900. We stopped the aircraft abeam Gate XY and set the parking break. The FO (First Officer) contacted Operations and they informed us that Maintenance was going to move the CRJ900 off our gate. Maintenance pushed the aircraft off our gate and proceeded to squeeze the CRJ900 between our aircraft and Gate XY. We were stopped on the ramp taxi line abeam Gate XY with both engines running. We contacted Operations 2 more times demanding that they contact the push crew and have them hold position. We were concerned about wing tip and aircraft clearance. Operations said they would contact Maintenance but the push crew continued. We were shocked at the lack of aircraft and wingtip clearance as Maintenance pushed the CRJ900 to the right of our nose abeam Gate XY. Cause: We are unsure of why Operations was not able to stop the push crew...comm between Operations and Maintenance at ZZZ should be investigated.ZZZ Maintenance pushed the boundaries of safe wingtip and aircraft clearance during the push...ZZZ push crew Operations at should be investigated.