First, there's a conflict between a whole mythology of self-reliant individualism, in which problems are solved by creative entrepreneurs and the free market, vs the state, who in this case are restricting a whole range of freedoms and, preventing people from making a living, in the name of public health, and in this case they're trying to tell people what to wear.
Second, there's a related conflict between the idea of the individual being responsible for his or her own health and that their family and friends, and deciding what protective measures are and aren't necessary, and that of the state mandating that everyone must wear protective masks not only for their protection, but also to protect everyone else.
Ask yourself, how would Ayn Rand's fantasy objectivist supermen like Howard Roark have reacted to a pandemic, and what would he have done had some politician tried to tell him what he could and couldn't wear, and what sort of measures he should take to protect his health, or that of his customers, employees, or even people with whom he had no dealings whatsoever?
They used to worry, way back when, about the deleterious effects of sex, drugs, and rock and roll, on the younger generation, along with cultural marxism and video games.
As it turns out, it's all those teenage American boys jerking off as they read Atlas bloody Shrugged that we needed worry about -- see what they've grown into.