Commercial flying is safe with an ICD. Aircraft cabins are pressurised to an equivalent altitude of around 6,000 to 8,000 feet, well within the range that ICD devices are designed to operate in.
For high-altitude activities such as mountain hiking or climbing at significant elevation, the considerations relate more to your underlying cardiac condition than to the device itself. High altitude reduces the amount of oxygen available, which increases the workload on the heart and can, in some conditions, increase arrhythmia risk. Whether a specific altitude is safe depends on your diagnosis and your current level of fitness. Discuss any planned high-altitude activities with your cardiologist before going.
For unpressurised light aircraft or skydiving, some ICD manufacturers specify altitude and pressure ratings for their devices. If you are involved in aviation, contact your ICD clinic and the device manufacturer directly for guidance specific to your model, and note that the Civil Aviation Authority has separate requirements for pilots and aircrew with cardiac conditions.