Caveat: I strongly agree with wearing masks, and my own church continues to do so even though it is not required where I live. I am attempting to write this answer based on what I have heard from others, especially when some churches refused to close during lockdown. I very much disagree with the following, but it is an argument I have heard. In some cases, there may also be non-religious factors, personal beliefs, and sin that factor into decisions, which I will not be addressing these in this answer.
Then I saw a second beast, coming out of the earth. It had two horns like a lamb, but it spoke like a dragon. It exercised all the authority of the first beast on its behalf, and made the earth and its inhabitants worship the first beast, whose fatal wound had been healed. And it performed great signs, even causing fire to come down from heaven to the earth in full view of the people. Because of the signs it was given power to perform on behalf of the first beast, it deceived the inhabitants of the earth. It ordered them to set up an image in honor of the beast who was wounded by the sword and yet lived. The second beast was given power to give breath to the image of the first beast, so that the image could speak and cause all who refused to worship the image to be killed. It also forced all people, great and small, rich and poor, free and slave, to receive a mark on their right hands or on their foreheads, so that they could not buy or sell unless they had the mark, which is the name of the beast or the number of its name. This calls for wisdom. Let the person who has insight calculate the number of the beast, for it is the number of a man. That number is 666. Revelation 13:11-18 (NIV). Emphasis mine.
In this passage of Revelation, we are presented with an agent of Satan, who "deceives" humanity into obeying and worshipping Satan. They do so by imposing restrictions on "all people", which they're forced to obey in order to access basic necessities ("they could not buy"). Some people have historically interpretted the number of the beast, as well as other references to Babylon and Rome in Revelation, to mean the two beasts are metaphors for governments and other human authorities.
This has lead some people to reach the conclusion that the various Covid restrictions - mask mandates, lockdowns, and vaccine passports - are a manifestation of this prophecy. By complying, churches are aiding the work of Satan. Others are concerned that although these particular restrictions are justified, they set legal precedence for unjust restrictions, and so by allowing them, we pave the way for this prophecy in the near future. In the UK, several religious bodies started legal action against the government in order to stop this pattern (which, incidently, worked. Churches were allowed to remain open in subsequent lockdown). If this isn't possible, churches may visibly protest by not wearing masks.
So, in conclusion, some christians may see mask mandates as a tool of Satan to restrict the church of God, and that this was biblically predicted. These Christians would therefore feel it necessary to fight against these restrictions in any way they can - including public dissobedience.