These adjustments are more than just putting the distributive method into practice. If you have 2 separate time series which do not overlap and you are attempting to put forward a theory about the long-term trend of the underlying data, then you very much do need to provide a justification for any adjustment you make to each time series.

How does that even make sense? If the human activities at the airport location are causing an increase in temperatures at the airport, then that by definition is an increase in the temperature of the local climate.

Climate and local weather are not the same. If I build a parking lot the local temperature may increase by several degrees C on average, yet this represents an inconsequential change to the local climate within a radius of, say, 100km. More so, it represents an inconsequential change to the climate of the entire Earth. The significance of the urban heat island effect with relation to temperature records is that the proportion of weather stations which are affected by an increased urban heat island effect (due to increased urbanization) exceeds the percentage of the Earth affected by many orders of magnitude.

Yes, urban heat island effects can be accounted for, but I think the criticism is that for the most part they have not been.