The rule I follow is the same one I had for Y2K. If there is no interface to enter a date, you don't have to worry about it.
For example, on the sensationalized "documentaries" we had leading up to Y2K, they showed a stream of appliances and gadgets that had processors in them -- hair dryers, microwave ovens, dishwashers, food processors, etc saying they all would be vulnerable. Some of these display the time, but I haven't run across a microwave yet that accepted a date input.
This is great for thinking about the non-internet connected devices. What's also interesting about this idea is that we can test what 2038 will be like by slowly shifting the time for certain networks forward to see if a subset of stuff will fail. If it does, we can resort to turning off systems.
For example, on the sensationalized "documentaries" we had leading up to Y2K, they showed a stream of appliances and gadgets that had processors in them -- hair dryers, microwave ovens, dishwashers, food processors, etc saying they all would be vulnerable. Some of these display the time, but I haven't run across a microwave yet that accepted a date input.