Principle of material objectivity is an obsolete term and should be replaced by principle of material frame-indifference.
Here is a precise statement of the Principle:
The constitutive laws governing the internal conditions of a physical system and the interactions between its parts should not depend on whatever external frame of reference[1] is used to describe them.
"I was responsible for introducing the obsolete term in 1958 and now regret that I misled a lot of people", Walter Noll.