The spread of COVID-19 has forced governments to impose unprecedented restrictive measures on their people. Lockdowns have been introduced in many countries, and most governments have decided to require citizens to wear masks. The current study characterizes users’ attitudes towards the face mask requirements introduced by the Russian government as a response to the COVID-19 pandemic. We study how they relate to other users’ characteristics such as age, gender, and political attitudes. Subscriptions to information sources serve as a proxy for users’ political attitudes. Our results indicate that men and elder individuals—demographic groups that are most vulnerable to COVID-19—underestimate the benefits of wearing face masks, comparing to young people and women who demonstrate a higher rate of approval. We also discovered that users in opposition to the Russian government highly approve of this anti-COVID-19 measure, a result that is quite counterintuitive since the oppositionists should, a priori, negatively perceive all measures taken by the government. Further, we developed a probabilistic model that fixes the relationship between pure types (conservative/oppositionist; reject mask-wearing/approve of mask-wearing) and derived the method of estimating its parameters. We obtained that an oppositionist approves of the face mask requirements with the probability of 0.95. For those who support the Russian government, the odds of approval are merely 0.45.