Judaism is a religion, and being Hebrew is an ethnicity. Both folks of the religion and the separate ethnicity are called "Jews". I get that you don't want to recognize the ethnicity, but in today's society, and among racist jackwipes, the reality is most folks do.
I think if a person responded with 'I'm Hebrew', I would register that as a Location rather than a Religion.
Like, if a person said "I'm Catholic", wouldn't tell me much. Saying "I'm Italian" would.