It isn't the community's job because it is no job at all. Property rights, living rights, trading rights, and travel rights are all pretty fundamental and it requires no effort to not interfere in them.
Wrong. It does require efforts to support these legal rights. Property rights require assignment of rights to a scarce public resource (land). Property rights require ownership records, police and courts to protect, and support infrastructure. Travel requires maintenance of roads.
They are not human rights; or more specifically, they are not among the inalienable rights. They are rights that can be and are withheld, not given to, or taken away from people.
Property/travel/trade rights are frequently withheld from people who fail to pay taxes, fail to appear when summoned by the court to appear, or who fail to meet other standards or fulfill other duties that have been imposed upon them; Even people travelling in a dangerous manner, can lose travel rights due to DUI, can get fines for speeding --- ultimately resulting in restriction of travel (loss of license), or jail time, in some cases.
Refusing to take vaccinations is really no different fundamentally from refusing to do other thinks required.