why doesn’t the bar on the squat rack tip over when the weights are uneven?

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When loading/unloading the bar it can have a hugely uneven weight distribution. What is the physical mechanism that keeps the bar in the same place and stops it from tipping over?

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Tipping over is a matter of torque, and torque involves both force and distance.

The heavy plates are near the point where the bar rests on the rack. Torque is force times distance, and while the force of gravity on the heavy plates is large, the distance between the plates and the rotation point is small, so the torque in that direction is medium. The other end of the bar is not as heavy, so the force of gravity is smaller, but the distance between the far end of the bar and the resting point is large, so again, the torque in that direction is medium. So, they cancel out, and the bar doesn’t tip.