I have no problem at all with such things.
It's how things were done for hundreds of years before anyone thought of making the government the default source for everything. Opposition to collectivism in government does not automatically mean there should be no such thing as cooperation, community, or charity.
The key factor is the lack of force in the associations.
There is a strong tradition of community and family organization in the Asian community around here, but nothing as formalized as what you describe in health care.