Here, however, we're talking about a highly contagious virus that's transmitted through air, which can be spread even if you don't have symptoms and even if you don't actively interact with someone (as opposed to, say, HIV). Vaccines seemed to lower the spread risk, although with the new variant that effect looks weaker. So deciding for yourself to not vaccinate has a high likelihood of effecting others.
To go back to the road analogy, this doesn't look so much like a nanny state as setting some ground rules. Like driving on the same side of the road, mandating lights, blinkers, etc.
I am in no position to make an informed decision on these vaccines and measures by myself, so I trust those who actually know what they are talking about.
How do you fight that kind of thing?