Employers and renters won't do that because, as Charlie Wilson said (or Tom Hanks anyway), "it's against a shitload of really good laws."
Wouldn't it be legal for an employer or renter require that the persons they hire or rent to be American citizens?
That is illegal. Equal opportunity act and fair housing act both protect against discrimination on the basis of nationality. Edit: Sorry, there is no equal opportunity act. The employment discrimination was oulined in the civil rights act
Yes, you couldn't discriminate against an American citizen because he is Irish, German or Arabic but it would seem that non citizens wouldn't have the same rights