Can majoring in Ethnic Studies and taking the core courses for med school make me stand out for med school?

It's best to simply pursue what you like. I know this is trite, but passion makes you stand out more than anything else. Don't do it if you're trying to pad your resume or make yourself "stand out." It won't help you if you hate it, and it will be worse if you're bad at it. Admissions offices can smell fake from a mile away. They have thousands of people to choose from for a hundred something slots, and they don't have to pick you if they just don't like you.

But, if you love ethnic studies (I honestly didn't know it was a major...but sounds interesting!), and you love medicine, go for it.

Also, if you truly love the subject of medicine, don't feel guilty about majoring in biology or biochemistry. Half of medicine is biology--so if you love it, study it! But, medicine is also an art, and non-traditional medical students are definitely valuable in medicine. So definitely, do ethnic studies if you love it. But don't do it just to get into medical school.