According to Vaccines Today, herd immunity occurs when a significant portion of a population (or herd) that is vaccinated "provides a measure of protection for individuals who have not developed immunity." In other words, some people don't contract diseases even if they aren't immunized because so many others are immune to it, leading to decreased rates of infection. If this concept were to be true, would it ultimately be acceptable for some people to not be vaccinated?
Source: https://www.vaccinestoday.eu/stories/what-is-herd-immunity/
Herd immunity can produce negative consequences, specifically when it invokes "free-riding" behavior. Because herd immunity only works when most, if not all, members of a community are vaccinated, when people decide to forgo vaccination because they know others are vaccinated (free-riding), there is a detrimental effect on the overall health of the community, as well as on the individual members of that community. An individual's risk for infection depends on other individuals' vaccination status.
The issue of free-riding, then, brings the discussion back to the ethics behind vaccination. It requires us to question: Who bears the burden of vaccination and who benefits from herd immunity? Should individuals be allowed to benefit when others assume some level of risk (e.g., from vaccination) and they do not?
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4815604/
http://vk.ovg.ox.ac.uk/herd-immunity
I think that's definitely the derived question—who is "bound" to vaccinate his/herself or his/her children and who is "qualified" enough to not go through vaccination? After all, according to numerous comments within this post, it's clear that a "herd" or a "group" of individuals that are vaccinated can prevent the contagiousness of a virus/bacteria, even if there are a meager few who decide not to. This ultimately leads to a question ethics too, because that means some people NEED to vaccinate themselves/their children even though they necessarily don't have to (if there's at least >95% of people who are vaccinated) merely due to their financial status while others simply benefit from this situation. This is no different than commensalism. It sounds a little outlandish to me because there would be absolutely no way that all severely-low income families get away from pricey vaccinations; some families are required to be vaccinated even if they're financially capable because there's going to be at least one family that decides not to. It would be interesting to see what the government comes up with if there ever happens to be an argument of "vaccination burden."
Here's a graphic from IFL Science that illustrates how herd immunity works. The red lines demonstrate the spread of the infectious disease, with blue dots symbolizing unvaccinated people and yellow dots symbolizing vaccinated people. As you can see, diseases spread much slower the more people are vaccinated. In the final scenario, the unvaccinated people (which can represent people with autoimmune disorders who can't be vaccinated) can rely on everyone else in order to stay uninfected.
https://www.iflscience.com/health-and-medicine/this-gif-only-takes-6-seconds-to-show-how-herd-immunity-works/
If you've ever been forced into a group project, you probably know how much you want to metaphorically strangle your teammates when it looks like they're off in the corner picking their own nose. It is both ethical and practical to pull your own load, and people absolutely need to do so.
That being said, relying on herd immunity as a form of vaccination isn't the best, and certainly shouldn't be seen as the number one solution, but in a world that pushes socioeconomic groups farther and farther apart, we might have the face the fact that herd immunity is a major benefit for people who are unable to afford vaccinations. Socioeconomic mobility (the ability to move up 'ranks' in a society's hierarchy, e.x. moving from the middle-class to the upper-class) is an increasing problem in America and countries around the world, but along with that, the price of vaccination has sharply increased in the past two decades, the cost going up from single digits to triple digits. Yes, we could go into the moral argument of whether or not parents should vaccinate their children, and they most definitely should, but the reality is that not everyone has the means to do so.
https://www.nytimes.com/2014/07/03/health/Vaccine-Costs-Soaring-Paying-Till-It-Hurts.html
This specific topic interestingly enough came up in one of my Lincoln Douglas debate resolutions 'Resolved: Public health concerns justify compulsory immunization'. So my knowledge of herd immunity is based around a moral, conceptual concept, one of which is this idea of 'fairness' or justice that you mention in the question.
In a general sense, having seen both affirmative and negative sides in the resolution (note that in this debate resolution 'herd immunity' was a major clashing point), it really isn't 'fair' in the social, collective sense for one individual to forgo immunization. If you look at famous philosopher John Rawls' Social Contract, he specifically says that justice exists with fairness, wherein fairness consists of a society that protects even the weakest, most vulnerable individuals to the best extent it can, with both government and citizenry working together for that goal.
That means we're talking about people whose bodies cannot take vaccinations, people who perhaps can't even afford vaccinations, and many more cases. And it quite literally is scientifically proven that 'herd immunity' works, and works when the population vaccinates over a certain population percentage. What all of this means is that not 100% of people need to be vaccinated, and, in my belief, only those with legitimate justifications for not taking vaccinations should not, providing protection to all and fulfilling your question about 'fairness' and 'justice.'
So, to answer your question directly, yes, it would be fair for some people to not be vaccinated. But only considering the qualifier I've explained above. I will note, though, that this is only in the specific case of Rawls... I think you'd find John Locke and his libertarian conception of individual liberty above all would quite frankly disagree with the answer I gave based off of Rawls.