Air carrier Captain reported they transmitted 'Stop Stop' on Ground frequency during push back when they observed another aircraft pushing back from the adjacent gate at a high speed towards them.

Narrative

We (Aircraft X; ZZZ-ZZZ1) were given clearance to push from gate XX in ZZZ to spot XX. Soon after we began our push; Aircraft Y; started to push off of gate XY. Initially; when Aircraft Y started pushing; it looked like the push crew was pushing tail to the east (towards the alley exit). Then the push crew started pushing their tail back towards us. We became concerned; as their push crew started moving faster and faster. I told our tug driver to watch for the aircraft behind him. He thought I was speaking of an aircraft behind us (there was not one). With increased urgency; I told him the aircraft behind him; as he sat in the tug. They were pushing way too fast and the closure rate made me uncomfortable. I told our tug driver to stop the push (we were just about on centerline); as I felt Aircraft Y was going to be pushed into us and thus; he would have been injured. While this was all taking place; FO (First Officer) said their wingman (aircraft left) was holding his wands up in a crossed position; indicating to the driver to stop. There was no response from the driver and the wingman started jumping up and down trying to get the driver's attention.I got on ground frequency and said Stop! Stop!" Eventually they did stop the push. FO; queried Ground Control about how quickly they were pushing. I believe their response was something like "Oh; you need more room?" Then Aircraft Y was given clearance to pull up to spot XY.Our tug driver indicated that the push crews are supposed to move aircraft in first gear and said that the Aircraft Y tug driver was clearly not in first gear. He too; was not happy with the situation. He did indicate that there was a manager on the ramp at the time and he expected him to have a conversation with the push crew (Aircraft Y's) when they got back to the gate. We did not see this happen. I asked our tug driver to please go have a conversation with his manager and try to get the situation addressed so that this behavior is stopped. FO and I sat for a moment after this. I said to him that "Never; have I been so afraid about being involved in an aircraft incident/accident." He agreed. We collected ourselves and verified that we were both okay and able to safely continue with our day. Cause: Factors: Lack of SOP compliance for push crew on gate XY. Mitigation: Continuation of training and supervisor presence on the ramp."