I was at a meeting of Catholic men a few weeks ago. I was the only 'Traditional' Catholic present and yes they are aware of my position. One of the gentlemen espoused the view that the Pope cannot teach error in an encyclical. Knowing that, strictly speaking, the Pope does not automatically invoke the power of infallibility when he lifts his pen to write a letter, I entered into an argument. I argued from the point of Vatican I's declaration on infallibility, but he remained unconvinced. Later, I did a search and found an article by Msgr. Fenton (see below) the outlines much about the authority of encyclical letters. A brief summary is that it is possible, but unlikely, for encyclical letters to contain error. Source
Seeking A Way Forward: A Lay Catholic Traditionalist's Thoughts and Reflections on ways to help the Church emerge from this crisis of Faith