Not so hypothetical

Say you are an employee of a museum controlled by the federal government, working in the conservation department. Let us assume further that you are female, as are all other members of the conservation department at this museum. An Indian artifact belonging to the museum needs to be conserved, but according to the members of the tribe that created the item, this artifact is a "male object" and may only be handled by men.

Is it legal, under currently existing antidiscrimination law, to prohibit female employees from conserving the object and to transfer you to another museum for one week in exchange for a male conservation employee from that museum? (The male employee is permitted to conserve the object and then returns to his home institution.) Should such catering to the religious/cultural prejudices of the creator tribe be the policy of our federal government? Does your answer change if the item is still owned by the tribe but they wish to permit its display subject to the condition that it only be handled by men?

UPDATE: Curtis references NAGPRA, which apparently establishes that the museum doesn't really own any of the sacred objects in its collection in the first place. The relevant law with respect to this particular museum can be found here. I think the substance with respect to this issue is the same in both pieces of legislation.
UPDATE II: An actual employment law type person weighs in.