The monastic rules of the Vinaya has rules pertaining to food, lodging, medicine, conduct etc. There are rules pertaining to medical care. The Buddha ate, slept, wore robes, took medicine when he was ill etc.
The Middle Way of the Buddha avoids both extreme indulgence and extreme asceticism. It includes moderation in food, healthcare and living. To neglect healthcare is to go against the Middle Way of moderation.
From Kucchivikara-vatthu of the Vinaya, the Buddha taught:
"A sick person endowed with five qualities is hard to tend to: he does
what is not amenable to his cure; he does not know the proper amount
in things amenable to his cure; he does not take his medicine; he does
not tell his symptoms, as they actually are present, to the nurse
desiring his welfare, saying that they are worse when they are worse,
improving when they are improving, or remaining the same when they are
remaining the same; and he is not the type who can endure bodily
feelings that are painful, fierce, sharp, wracking, repellent,
disagreeable, life-threatening. A sick person endowed with these five
qualities is hard to tend to.
"A sick person endowed with five qualities is easy to tend to: he does
what is amenable to his cure; he knows the proper amount in things
amenable to his cure; he takes his medicine; he tells his symptoms, as
they actually are present, to the nurse desiring his welfare, saying
that they are worse when they are worse, improving when they are
improving, or remaining the same when they are remaining the same; and
he is the type who can endure bodily feelings that are painful,
fierce, sharp, wracking, repellent, disagreeable, life-threatening. A
sick person endowed with these five qualities is easy to tend to.
Based on this Vinaya quote, I would say that the Buddha himself would have wanted his followers to practice moderation, and accept the advice of healthcare professionals and the government when dealing with the Covid-19 pandemic.
Also, spreading misinformation about Covid-19, masks and vaccines is against the fourth precept of not speaking falsehood.
Wearing a surgical mask is more for the wearer to avoid spreading pathogens to others, than for the wearer's own protection from contracting an infectious disease. As such, wearing a mask with the explicit intention of reducing others' suffering, is also an expression of compassion (karuna).
The quote from DN 26 below, also shows that the Buddha did not promote anarchy. He stated that the wheel-turning monarch should provide just protection and security to his subjects and also care for their welfare.
‘But sire, what are the noble duties of a wheel-turning monarch?’
‘Well then, my dear, relying only on principle—honoring, respecting,
and venerating principle, having principle as your flag, banner, and
authority — provide just protection and security for your court,
troops, aristocrats, vassals, brahmins and householders, people of
town and country, ascetics and brahmins, beasts and birds. Do not let
injustice prevail in the realm. Pay money to the penniless in the
realm.
I would even say that a responsible Buddhist should support his or her government and follow its advice, if the government is discernibly doing the right thing, and if its advice is in accordance with the five precepts, Right Action, Right Speech and Right Livelihood. For e.g. conscription into military service is against Right Livelihood.
You can use these arguments to politely persuade monks and lay Buddhists.