Austenitic stainless steels have a high amount of austenite which makes them mostly non-magnetic. Even though grades such as 304 and 316 stainless steel have high amounts of iron in their chemical composition, austenite means they are non-ferromagnetic.
However, if the crystal structure of austenitic stainless steel is changed through work-hardening or special thermal treatment, then ferrite can form in some locations making the steel partially magnetic.