Well, there are multiple levels to your answer just like there are multiple levels to your question which you also did not focus on. It is a private transaction so any store can adopt policies for non-cash credit transactions they want (not for debit cards). HOWEVER, having been in a few Dallas area Walmarts (like West Plano, etc.) I swiftly realized they do things a bit different than the stores around most of Houston. I don't remember ever seeing Ralph Lauren clothes being sold here...
The answer: Under Federal Law all places of public accommodation and sales can not treat people differently based upon their protected status involving National Origin, Race, Religion, Gender, etc. Additionally, under the US Constitution, there is no difference in the application of such law on the basis of citizenship. All persons on US lands are governed by the same US laws, citizen, non-citizen, even Martians (if they don't zap us first)! We fought a war that killed or wounded several hundreds of thousands of our own Citizens to make sure the word "people" extends to all people, not just a selected few. Yet the treated you differently and you are a US person under the Constitution. I am sorry.
You have potential legal claims under Federal Law. You really should talk to a Lawyer who has a feel for social justice as soon as possible in your area, or if not, in Houston or San Antonio. I am opening a part time office in Dallas in a week or so as well.
You need a lawyer, not an activist who gets on TV and promotes himself at your expense and suffering. I am doing a discrimination matter this week involving a pizza delivery that insulted the person's race and religion written under the top of the pizza box. It still happens. I also have a very wealthy African Doctor client whose teenage some gets stopped and search when he goes into stores in wealthy neighborhoods (where he lives) and I help him often. It is very sad for all the people... Interestingly, in the languages of many American Indian tribes from thousands of years before they were made citizens in the 1800's, the word for nation was exactly the same word as the word for "people"... all people were... the nation. Please take some action to make this a better place for all people.
Because you were buying even milk something covered under the Federal WIC program in which they participate, they are vulnerable. Also, the majority of Wal-mart's sales in much of Texas is to minority customers... it would seem like they want to resolve this quickly. PLUS there are multiple video recordings on each cashier so there is evidence of it all PLEASE CONTACT LAWYERS BY EMAIL EVEN THIS WEEKEND!!
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If you have signed the back of your credit card, then pursuant to credit card merchant policy, they cannot ask for additional ID. If you had not signed the back of the card, then it is completely permissible asking for additional candy. If it is both a credit card and debit card, then of course you could have used the debit card without any id. What kind of credit card was it? Had you signed the back of it?
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