While it is true that 300 series stainless is non-magnetic, if the material is heavily drawn or by another method, heavily cold worked it will attract a magnet. That said, it will not attract like carbon steel, but it will attract more than you would expect.
The austenitic steels are nonmagnetic (or paramagnetic) - ie either they are not magnetised or are slightly magnetised in presence of the field. The 300 series are basically in this category.
The ferritic and martensitic steels are ferromagnetic.
In case of some manufacturing problems if the austenite of your SS converts to martensite fully or partially, you may get a magnetic material.
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