Most major scientific journals now require data archiving after publication. Many require it for review. So anthropology must figure out how to responsibly provide access to data. Luckily, other fields have already invested a lot in figured this out.
The important thing to realize is that providing access does not mean complete loss of control, either for the communities that provide the data or for researchers. For example, access can be restricted to researchers affiliated with research institutions, and limits can be placed on rights of reuse. But some level of access is necessary, if for no other reason than to allow other scholars the ability to verify our analyses. At the same time, researchers who want access to data must respect that data are political and continued collaboration with communities that provide data requires privacy and limits on reuse.
A standard data sharing memorandum grants all collaborators non-exclusive use of the data for scientific analysis