Reciprocity
There is a long-term reciprocity lurking behind this community stuff.
It’s totally OK, even a pleasure, to cover for someone. It can even be someone that never covers for you, as long as she covers for other people in the space (however you define its borders). So it is network reciprocity. But if you get the idea that someone is a free rider, then covering for her is not so OK anymore. It can only be OK if you really live in abundance, and it does not matter. But most of us are a long way from there.
Community care takes away the externality of health care (“the person that demands the care is not the person who is footing the bill”, as @Lakomaa likes to say). Tradeoffs become very explicit. The best example I have seen of this is the discussion of health care in Amish communities in the US. Amish refuse insurance (“it de-responsabilises people”). So, when a person gets sick, the church collects alms to help her front expenses. But this might happen at a time when the community might be facing other expenses (“setting up a farm for a young couple”). The community needs to decide what to do. The bottom line is: Amish people focus on preventative health care, because it’s irt cheap and effective, and if they fall sick they are imposing a burden (however welcome) on their brothers and sisters. In other words, though the individuals are generous, the community does the economically efficient thing! The whole story is here.
Additionally, the cultural evolution theorists like Wilson claim that we are hardwired to find and drive out free riders because of evolutionary pressure at the level of the group. This theory is super-fascinating, and deserves its own discussion, so I will just leave it here. It might help to explain why you prefer to help people who share your values.