An assembly is provided for rotational equipment. This assembly includes a stationary structure, a rotating structure, a seal element and an anti-rotation lock. The rotating structure is rotatable about an axis. The rotating structure is configured as or otherwise includes a seal land. The seal element is configured to seal a gap between the stationary structure and the seal land. The seal element extends circumferentially about the axis. The seal element axially contacts the seal land. The anti-rotation lock projects radially into the stationary structure and the seal element. The anti-rotation lock is configured to at least substantially prevent rotation of the seal element relative to the stationary structure.