In spite of a growing body of scientific evidence on the effectiveness of individual face mask usage for reducing transmission rates, individual face mask usage has become a highly polarized topic within the United States. A series of policy shifts by various governmental bodies have been speculated to have contributed to the polarization of face masks. A typical method to investigate the effects of these policy shifts is to use surveys. However, survey-based approaches have multiple limitations: biased responses, limited sample size, badly crafted questions may skew responses and inhibit insight, and responses may prove quickly irrelevant as opinions change in response to a dynamic topic. We propose a novel approach to 1) accurately gauge public sentiment towards face masks in the United States during COVID-19 using a multi-modal demographic inference framework with topic modeling and 2) determine whether face mask policy shifts contributed to polarization towards face masks using offline change point analysis on Twitter data. First, we infer several key demographics of individual Twitter users such as their age, gender, and whether they are a college student using a multi-modal demographic prediction framework and analyze the average sentiment for each respective demographic. Next, we conduct topic analysis using latent Dirichlet allocation (LDA). Finally, we conduct offline change point discovery on our sentiment time series data using the Pruned Exact Linear Time (PELT) search algorithm. Experimental results on a large corpus of Twitter data reveal multiple insights regarding demographic sentiment towards face masks that agree with existing surveys. Furthermore, we find two key policy-shift events contributed to statistically significant changes in sentiment for both Republicans and Democrats.