Should Christians Claim Exemption from Mask Mandates?

Several state governments and some big cities reimposed mask mandates this summer and fall as the highly infectious Delta variant of COVID-19 spread through the United States. Some of these local governments -- including a county in Ohio, a school district in Missouri, and the state of Virginia -- allow citizens to claim a religious exemption from the mandate. Should Christians claim this exemption? Are there grounds for claiming that masks violate our Christian faith?