So if you don't wanna get vaxxed, with an experimental vaccine, then you shouldn't care if someone else gets it.
A different way to look at it--we should always care if someone doesn't or does get a vaccine. The ramifications of just how many people get a vaccine varies.
That's one of the biggest determining factors.
Right now with COVID the ramifications is mask wearing, social distancing, stay at home orders, job loss, increased food insecurities, inability to pay rent or mortgage, loved ones passing away with no one there, loved ones not being able to be seen (or chosen not to be seen out of concern over health risks), industries virtually decimated (especially travel), economies impacted to a large degree overall, people's income disrupted due consumer behaviors and in certain situations restrictions are causing that, movies keep being shifted forward in time and the movie theater industry is hinging on collapse, immunizations of other diseases, routine healthcare, disease screening and treatment in some cases, surgeries, and so much more it would take forever to list it out. That's literally just the U.S...look outside the U.S. and you'll find the same and more.
Now yes there will likely be a line in the sand where some of these things will simply stop but the consequences of so much of the stuff won't just go away. They'll be felt for a long while.
We always should care if someone gets a vaccine but right now with COVID the stakes and the ramifications carry quite a lot of weight.