Yes, F and T are both "J" functions--they construct a structured, organized model that is used to judge themselves and the world around them.
Because the model is structured and fairly rigorous, there occur anomalies like you mentioned. The model is rather inflexible, so it misses some things (for example I'm usually polite but rarely courteous) and gets injured or stressed by others. When others violate the principles of the model, I may lash out or I may simply dismiss the other--I may decide that the other person is no longer part of my world.
Like you said, it's traumatic when I myself can't live up to the model. So over time I've built a lot of cynicism and selfishness into the model just to keep it workable and applicable to the real world and my own capabilities. Otherwise the model can turn into a straitjacket and make action or interaction impossible, leading to a lot of frustration and anger.