This "othering" of non-Whites probably happens outside of conscious awareness a lot of the time, but once a person does become consciously aware s/he's using marginalizing language, it's important to stop.
Sometimes the language we Americans use when talking about race/ethnicity is just awkward or inaccurate.
This term is almost always used by Whites to refer to a person who is thought of as the quintessential representation of an American citizen. The "All American" person being described is almost always mono-racially White, and most often has blond hair and blue eyes - a combination of traits that even most Whites don't have.
The term "All American" renders minorities - including actual Native Americans - politically invisible.
There are reasonable ways to use this word:
There are many ethnic groups inhabiting the world.
He wanted to know if ethnic differences fueled the conflict between the warring tribes.
I don't like ethnic food. I only eat American stuff.
Where's the ethnic hair care aisle? ... My step-daughter needs hair grease.
Everyone is "ethnic" because each of us has at least one ethnic heritage - that includes all Whites/European Americans. Likewise, everyone's food, clothes, etc., is "ethnic". It's therefore ignorant and exclusionary to label someone else's people, culture, food or hair products "ethnic".
In addition, "ethnic" may signal disinterest and laziness in discerning a non-White person's ethnicity or culture:
The Nobel laureate this year is some ethnic guy from New Jersey.
(It's easy to wonder whether or not the speaker cares if the non-White person is Puerto Rican, African or Greek.)
Sometimes the word is used euphemistically, like when a person is actively stereotyping someone non-White, or being racist, but wants to try and use sneaky language to sound less offensive:
Could you act more ethnic? The audience needs to know your character lives in Chicago.
Well, your skin tone is a little ethnic, but other than that you're attractive.
"Person of color" / "People of color"
This term is popularly used by Whites and non-Whites to refer to anyone who isn't entirely White. "People of color" sounds absurd to my ears. With the exception of albinism, everyone has skin pigment/color.
"People of color" is an inversion of "colored people", a term that fell out of favor decades ago (except, ironically, with the NAACP), and is currently considered racially derogatory.
Why is "people of color" any more acceptable than "colored people"? Why is it that people with only about 1/4 non-White ancestry (like Shailene Woodley or Wentworth Miller) are called "people of color"? The label is used to separate out mono-racially White people from anyone who has any known non-White ancestry at all, and therefore "people of color" is an identifying term that promotes the racist One Drop Rule. There are the "pure Whites", and then there's everyone else (coloreds); a subtle reminder of Jim Crow's segregated South, with those "Colored Only" signs.
There are two absurd classifications for people I heavily rely on for both the title of my blog and its contents: "Black" and "White". Just as we all have skin color, very few of us are literally Black or literally White. Both terms are polarizing and invoke images of contrasting ethnic physical differences that are exaggerated. I'm ambivalent about my use of either term and continue my search for alternative descriptors.