Fair Housing

Do not think so. "Immigration Status" does not mean a lack of US credit history. Without the credit check, the landlord will have no way to determine credit worthiness. Everyone needs to go through the credit check regardless of who they are.
https://www1.nyc.gov/assets/cchr/downloads/pdf/publications/FairHouse_Pamphlet2016-English.pdf

I understand that part, but once you establish a strict requirement that for sure and by default cannot be satisfied by someone who is from another country in my opinion you are in violation. A landlord can ask the rent upfront in case of bad credit history, but the idea that one MUST have US credit history to apply is and again in my opinion a discrimination.

Law does not prohibit credit check in any way.

You are missing the point. Let's say that you are relocating from another Country and that you didn't live in the US before, which is true for the vast majority of the foreign nationals.
Would you be able to rent this apartment? No you wouldn't.
Not even if you pay the whole rent upfront. And that is a clear discrimination even if running a credit check is not illegal the effect of this kind of requirement is to create a discrimination (national origin), in my opinion.

I understand your point but I believe law does not prohibit credit check and does not state foreign residents are protected class. There are plenty of people with say Chinese national origin who will satisfy the US credit check requirement. Perhaps others on the board have more experience.

I looked at the brochure:
1) National Origin is listed, has protected status.
2) You have the right to see all available housing, you cannot be limited or steered to a particular area,
neighborhood, or APARTMENT
3) You cannot refuse to RENT, charge higher rent, impose additional fees, offer different services or access to facilities, or fail to make repairs based on any resident’s protected status under the law.

The credit history is important and I understand Landlords, but this violates 1,2,3. Why? Because using a lawful requirement creates, even if indirectly and unlawful consequence. It is so clear to me. If a Landlord want to be protected and again I respect that, he/she MUST give the option to pay the rent upfront, but rejecting by default people with no US credit history (excellent) is really nasty.

Non US national origin does not mean a lack of credit history. I will let others on the board comment.

Some more definition of “National Origin”.
https://www.equalhousing.org/wp-content/uploads/2014/09/2012-Immigration-Status-FAQ.pdf

The requirement for a "ESTABLISHED, EXCELLENT U.S. CREDIT HISTORY," discriminates only in credit rating - it discriminates equally based on financial criteria that are neutral to national origin. It's an *easier* hurdle for those who have been in the US for a while (and those who are older), as they have had longer to build a "U.S. Credit history" but, as previously noted, does not discriminate against any class of non-residents who have a US credit history.

One could say the credit check discriminates against most 21 year olds with no job history.