Despite the reality that in the United States "freedom" doesn't mean and rarely has ever meant that we have license to do whatever we want to. There are speed limits, zoning laws, taxation, regulations of various kinds, licenses and fees required for many professions and activities. Even though untrammeled liberty is more a fantasy than a reality, our culture persists in elevating personal freedom over community responsibility. Virtually every religion makes a virtue of altruism, taking care of your brothers & sisters is admired, the Good Samaritan parable is held up as aspirational; yet when push comes to shove, it's "look out for number one". If Americans believed their own mythos of community and valued it over individualism, they would be glad to do whatever it took to protect, not only themselves, but the greater community.
There are times when we cannot depend on private businesses or individuals to do the right thing. Read up on the history of the labor movement and the growth of unions in this country. Businesses didn't do the right thing. People were worked to death, sometimes literally; there were no safety regulations; pollution via the waste products of various industries was rampant; there was literally cocaine in soft drinks and "health products"; and must I remind you, a lot of people were enslaved! There are times, when for the greater good, government, as the representative of the people and the steward of our well-bring, must step in and legislate, direct, or mandate what individuals or corporations are unable or unwilling to do. The partial mandate that people get vaccinated or suffer various consequences is not a new phenomena, but consistent with historical public health or other emergency measures.
In my opinion, cries of "freedom" are only an excuse and don't tell the whole story. The other part of the resistance to vaccination and common sense protective measures is an hysterical belief that the people who have spent their lives becoming experts either don't know what they're talking about, or are lying in order to exert some ephemeral control over the populace. While eschewing the expertise of those who know what they're talking about, they latch on to unproven remedies and conspiracy theories. They search for the tiniest of problems and blow them out of proportion. They readily accept the craziest and most implausible of stories while claiming to be skeptics who don't follow the government like sheep. If these irrational anti-vacciners had complied with public health measures instead of hysterically digging in their heels, we likely wouldn't need mandates.
The vaccines are not experimental. They have been tested and approved. Are they 100% effective? Do masks protect us completely? No and no. What is effective is a combination of widespread vaccination, mask wearing in public, social distancing, and sanitation. If large segments of the population refuse to take any of these precautions, the virus will continue to mutate and spread. With the exception of the small percentage of people who are medically unable to get vaccinated, the anti-vaxxers are just plain ignorant and are contributing to the continued spread of Covid-19.
Their objections are based on ignorance.