The most relevant might be Luke 5:31:

Jesus answered them, “It is not the healthy who need a doctor, but the sick.

Which meanwhile is being completely ignored. Quarantine is also meant for sick people.

And the concept of Corona is nothing new at all: https://de.wikipedia.org/wiki/Corona_(Heilige)

However, the Torah hits the nail:

Two words in Hebrew describe a mask – masveh and masakh.
We find masveh in the Torah: following the sin of the Golden Calf.

The Clear Biblical Basis

The primary motivation for civil disobedience by Christians can be found in Acts:

This is the primary motivation cited for Biblical civil disobedience. There are, however, other factors involved, especially in the United States, which may be more prevalent among Christian populations even though not directly inspired by Biblical motivation.

In the passage in Acts, the "obey God" was referring to God's command to spread the Gospel. It showed that when God gives a specific command, the government cannot override that command, and in particular, God has commanded us to always spread the Gospel. This seems to be in line with other Bible accounts of commended civil disobedience, such as those in the book of Daniel.

Essentially, if the government ever tells you to stop preaching the Bible, you still preach the Bible.

The Cultural and Historical Context

To fully understand the common justification to compare COVID mask mandates with Biblically sanctioned civil disobedience, it is important to consider the cultural context. The United States has historically been a Christian Nation, but the influence of Christianity has waxed and waned through different periods creating a unique culture. In particular, because of influence during the 1970s and 1980s there has been the growth of a particular culture in America which can often conflate Christian religion and doctrine along with conservative and patriotic politics. In practice, what you are seeing is this mix playing out in public life.

Jesus' direct example regarding politics was to simply "render unto Caesar what is Caesar’s" and then generally stay out of politics, as in this example in Matthew (emphasis mine):

However, modern Christian Conservatives in the US hold to patriotic ideals that include the belief that the US government was itself a gift from God, and that the founders had passed on a stewardship to future citizens which require them to be active in government as part of what they are rendering unto Caesar. They believe active involvement is what the government asks of them, and that it is in this manner that will preserve the freedoms that God originally granted on the founding of the nation.

Unfortunately, this can muddy the waters a little, and it can potentially lead to conflicts where one must weigh actions across a spectrum. On the one end there are clearly Biblical imperatives such as "Don't stop preaching the Gospel", and on the other are political positions with only vague Biblical support based upon supposed contextual obligations, such as "Don't allow the government to take away God-given freedom".

Adding to this, there has been a more recent cultural shift away from what this Conservative Christian culture sees as both Christian and historically patriotic, primarily by politically progressive influences. The consolidation of power and growing influence of secularization in sectors such as media and academia have bred distrust and a sense of antagonism to modern Christian Conservatives. Up to the point of the epidemic, there had already been actions seen as attempts to silence Christian voices, including the growing "cancel culture" and also political voices during that election cycle.

There are also a non-trivial number of Conservative Christians in this group in the US who hold to certain ideals, such as a plain-text reading of Genesis 1-3 which seems to contradict the ideas (Abiogenesis, Common Descent) which are prevalent and often cited as being foundational to currently accepted principals used by the current medical community. This may cause them to be more skeptical of that community than most other cultures. While they do not typically (depending upon the group) reject medical advice or treatment, they tend to often favor holistic approaches which rely upon God's providence in the creation of the human body, and are more likely to rely upon hygiene and prayer than the average person. These considerations certainly have an impact on how they might view the effectiveness of things such as mask mandates in the absence of clear medical information.

The Conflict

These cultural convictions came to a clash with the government during the COVID-19 epidemic. Amid this context of distrust and uncertainty, the government, as well as the medical industry, put forth several changing and conflicting messages, leading to further distrust and uncertainty about the motivations behind the political rules. Once mask mandates were becoming state-backed, there were many people who felt that the various rules were not being applied evenhandedly and impacted certain groups more than others. For instance, Walmart and McDonald's could remain open while other similar businesses were forced to shut down or change their business model. This lead to a popular suspicion that the laws were not being used to actually protect the public, but were, in fact, being used to achieve some hidden political agenda.

By itself, that would have only allowed for political dissent, with only the most vaguely perceived Biblical warrant, if any. However, the laws aimed at preventing or restricting social gatherings were viewed by many people within the mentioned political and cultural context mentioned as potentially being a direct attack upon Christian's right and duty to assemble. Many Conservative Evangelical Christians in the US would cite that duty from Hebrews (emphasis mine):

This might seem like a stretch, but consider that because of the distrust and uncertainty, not a few of these people considered masks to be a detriment to good health, and also consider that it had not been common pre-COVID for many of the people in these groups to gather virtually, and even those who do can consider the above command to require physical assembly. Also, if one considers that many of these Christians treat certain assemblies as needing to be free and unrestricted to the public at large, including unbelievers for the purpose of propagating the Gospel, then you can understand why they may not have been willing to enforce such rules.

It may also be of significant note that, in practice, many of these "rules" requiring masks or calling for restrictions were not actually laws. There were cases where these were merely suggestions which were made to look like law, and some were rules which only applied to certain contexts, or were not enforceable for other reasons, and the situation was updating regularly. In practice, I did not personally witness a single congregation break a law. Some did actually wear masks. Some chose not to do so but never had a relevant law apply.

Conclusion

Given the context and understanding of those United States Christians who believed not wearing a mask amid COVID-19, the primary Biblical basis held for civil disobedience was the imperative to preach the Gospel, the command to assemble together, and to some lesser extent, the belief that civil disobedience of this manner would be showing good stewardship of a gift they believed God had given them.

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.

I think the difference between Paul's exhortation to obey civil authorities by paying taxes in Romans and the type of civil disobedience MLK partook in, is that paying taxes to the govt does not violate God's laws. In contrast, oppressing our fellow humans because of race is against God's law of love in Christ Jesus. And we must obey God's laws rather than man's laws when there is a direct conflict.

With COVID 19, we should wear masks if the government mandates it and it does not violate our conscience. Paul says in Romans and Corinthians that it is not wise to violate our own conscience, because that is a sin for us. So the only argument that could be made against wearing masks is either that it violates God's law or a person's conscience. Wearing a mask during a pandemic obviously does not violate God's law. So the only valid argument would be that it is an issue of conscience.

You could try to argue that wearing masks is somehow physically harmful, but imho that requires ignoring the fact that nations where basically everyone wore masks in public for extended periods of time saw no severe side effects.

Caveat: I'm not saying that people should be allowed not to wear masks due to a concern for their conscience (that is a separate question). I'm more so saying that there is no other rational reason for being against masks other than an issue of conscience.