"Following the religion..." ...which says that an individual is Jewish if their mother is Jewish and so on.

I think you dont really understand the familial aspect of Judaism: it seems itself not as mere religion but as an actual family. The Judaic religion is in large part the tribal law code which provide the rules by which that extended family are meant to live their lives: the above is one of the oldest.

If you think that's racist then take it up with the Rabbi. He won't be really concerned with your points though because, well, your mother wasn't Jewish so your not family and they don't count.