At least they made the shackle long enough so it would be easy to cut it off.

This is also an excellent example of why context is critically important when making field observations. Meaning more is needed to be known about the purpose, function, and location of this door and the spaces it protects. Not all fire doors are located within a means of egress nor do all fire doors serve as an exit door or an exit access door. Some more common examples might include doors to hazardous areas, doors to non-exit shaft enclosures, communicating doors, doors to normally unoccupied mechanical/electrical spaces, or doors in occupancy/building addition fire separation walls in older buildings that are not located in or across a means of egress.

At first glance a fire door sign and a padlock would tend to be a point of concern for any competent inspector but further investigation and additional information is needed to factually determine if this door is code compliant or code deficient.