One of the main dimensions characterizing the unfolding of opinion formation processes in social debates is the degree of open-mindedness of the involved population. Opinion dynamic modeling studies have tried to capture such a peculiar expression of individuals' personalities and relate it to emerging phenomena like polarization, radicalization, and ideology fragmentation. However, one of their major limitations lies in the strong assumptions they make on the initial distribution of such characteristics, often fixed so as to satisfy a normality hypothesis. Here we propose a data-driven methodology to estimate users' open-mindedness from online discussion data. Our analysis - focused on the political discussion taking place on Reddit during the first two years of the Trump presidency - unveils the existence of statistically diverse distributions of open-mindedness in annotated sub-populations (i.e., Republicans, Democrats, and Moderates/Neutrals). Moreover, such distributions appear to be stable across time and generated by individual users' behaviors that remain consistent and underdispersed.