My mom is basically the female Hitler.

The word "Hitler" is overused. Unless your mom is killing people by throwing them into ovens, this metaphor is not appropriate.

The answer to your question depends.

1) How old are you and your girlfriend?
2) How dependent are you on your parents? Do you depend on your mother financially or for housing?

You paint an ugly picture of your Mom, and if it's accurate there's not much you can do about it (assuming you've already calmly expressed your feelings to her).

Has she told your girlfriend that she doesn't like her because she is Greek, or was that your bright idea of sharing?

If she's rude to your girlfriend, don't bring the girl to your home. It's not fair to her to subject her to your mother's lousy behavior.

My mother's family was Irish/Norwegian (both grandparents were immigrants), and they really didn't like Italians. I dated several Italian girls throughout HS, and they were always giving me grief about it.

They didn't have aa problem with African-Americans or any other nationality, which made the whole thing seem weird, as well as nasty.

Eventually I learned that they grew up right next to an Italian neighborhood in NYC, and always had trouble with the Italian kids when they were growing up. Who started the trouble is anyone's guess. I also learned that my great-uncle, a Norwegian tugboat captain in NYC was killed by the Mafia for refusing to pay protection money.

Hardly logical to assume that all Italians are bad because of past incidents, but sometimes these sort of animosities have a root that isn't simply hatred of someone who is different. Maybe if you talk to your mother about it you will be able to get a better understanding of where her bigotry comes from. It won't make it right, you may no longer think of her as Hitler.

Your Mom is a bigot and desperately needs education.

Ignore her if you are of marrying age. Tolerate her if she has financial power over you.

Don't bring people around her that she can insult.

She will not get to enjoy her grandchildren. Pity.

http://www.merriam-webster.com/dictionary/bigot

Does the relationship with your girlfriend have potential to become a long-term, serious one?

Does your girlfriend need to spend time with your mother?

If it's not necessary, keep your mother away from your girlfriend. If there are other, less bigoted, family members spend your family time with them - not your mother.

I was always very lucky that my parents were extraordinarily open-minded about friends/boyfriends, but I know that isn't necessarily the norm. I had an aunt who had a tendency to make somewhat disparaging/bigoted comments about people she hadn't even met - simply based on their family names. It was best to not even mention friends to her, let alone to consider having her meet them. Good thing we didn't live on the same continent.

Choose either or. Girlfriend. Family. Which is it.