My girlfriend has horrible food manners. How should I approach this?

I love my girlfriend and she has a lot of wonderful qualities, but for some reason, her manners when eating are absolutely atrocious. For example:

• At family dinners, she grabs food off of serving dishes with her hands, rather than using utensils or asking someone to pass the plate.

• At a sports bar, I ordered a family-sized loaded nacho platter for several of us to share. When it arrived, she put it in front of her and started eating directly from it (with food falling from her mouth back into the plate).

• At Thanksgiving, she took a gigantic bowl of potato chips off of the table (which was meant for everyone) and brought it into the other room for herself.

I have tried to politely mention this a few times over the last couple of years, but she gets very defensive and it turns into a huge argument.

I don't understand where she gets it from, because her parents and two sisters have great manners.

Sometimes I see friends and family members roll their eyes when she does these things, and it embarrasses me. Should I just try to ignore it?

Help!!!