Should we use commas before and after white people in the sentence below or not?
We white people look down upon an African-American boy, girl, man and woman as a potential criminal in this country.
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As you have structured the sentence you would use a comma before and after. I would reconsider the structure though.
Something like: As white people we look down upon... (The rest of your sentence)
I am not sure what you are working on but it may be helpful to denote this is an opinion unless you have statements supporting it later. Like if I just said "Cheeseburgers are very good." but didn't quantify I am not offering the reader any reason to consider that statement. If I said "Cheeseburgers are very good. Nationally 10,000 cheeseburgers are consumed a month. There are over 1000 different varieties of cheeseburger and in a national pole Cheeseburgers came in second only to Pizza in Favorite Foods."
Again I have no idea the basis for your question so that may be completely useless but I thought it would be worth mentioning if it is for a piece you are writing.
As far as I'm concerned, the phrase "white people" here is considered an appositive. If the noun being modified is too general, all you have to do is leave the appositive explaining it alone without placing any commas. However, if the noun is already specific, then commas are necessary. And in my opinion, the word "We" here is specific enough; therefore, commas are needed.