The COVID-19 pandemic has disproportionately impacted the lives of minorities, such as members of the LGBTQ community (lesbian, gay, bisexual, transgender, and queer) due to pre-existing social disadvantages and health disparities. Although extensive research has been carried out on the impact of the COVID-19 pandemic on different aspects of the general population's lives, few studies are focused on the LGBTQ population. In this paper, we develop and evaluate two sets of machine learning classifiers using a pre-pandemic and a during-pandemic dataset to identify Twitter posts exhibiting minority stress, which is a unique pressure faced by the members of the LGBTQ population due to their sexual and gender identities. We demonstrate that our best pre- and during-pandemic models show strong and stable performance for detecting posts that contain minority stress. We investigate the linguistic differences in minority stress posts across pre- and during-pandemic periods. We find that anger words are strongly associated with minority stress during the COVID-19 pandemic. We explore the impact of the pandemic on the emotional states of the LGBTQ population by adopting propensity score-based matching to perform a causal analysis. The results show that the LGBTQ population have a greater increase in the usage of cognitive words and worsened observable attribute in the usage of positive emotion words than the group of the general population with similar pre-pandemic behavioral attributes. Our findings have implications for the public health domain and policy-makers to provide adequate support, especially with respect to mental health, to the LGBTQ population during future crises.