303 and 304 share the same basic chemistry except that 303 has added sulfur for machinabilty; the sulfides are solid state lubricants and chip breakers.
Any sulfide exposed to the surface is a corrosion pit starter. So items made from 303 have poorer corrosion resistance, even if you specify having the optional 0.6% Moly addition. The media in which this corrosion occurs will experience a pick-up in iron ions as a result of the pitting. There is no prohibition against the use of this grade in direct food contact, however. NSF only stipulates a minimum of 16%Cr in the alloys.
If you want to use 303 but avoid the corrosion, take the final machined part and passivate thoroughly. You can find this procedure at the FAQ's of stainlesscenter.com.