The enacted federal legislation would disagree with you.
Considering that the statement that zddoodah made was that there was no right to be "given a credit card" his/her statement was right on the money. No law says that anyone has a right to a credit card.
There is the Equal Credit Opportunity Act which bars discrimination in lending practices, though "presence type" isn't exactly spelled out there, national origin and a few others are.
But you are right that the Equal Credit Opportunity Act (ECOA) does prohibit lenders from discriminating against applicants on the basis of, among other things, national origin. The problem is that national origin is not the same thing as citizenship status. That is why in the employment context, for example, federal law expressly bars most discrimination by private employers based on citizenship as well as on national origin. If national origin covered it, the addition of citizenship in the employment context would not be needed. Congress did not expressly add citizenship as a protected category in the ECOA, thus it appears that discrimination based citizenship is not prohibited by the ECOA
Whether immigration status can be considered in credit decisions isn't a decided thing yet in courts (though there is one case pending).
Actually, there are several cases that address this in the context of the ECOA. A federal district court dismissed a complaint complaining of discrimination on the basis of citizenship in a very short and succinct opinion, explaining:
While 15 U.S.C. s 1691(a) prohibits discrimination by a creditor against a credit applicant on the basis of several classifications including national origin, neither the statute nor its legislative history shows an intent of Congress to proscribe the denial of credit on the ground of lack of citizenship. Moreover, the regulations promulgated pursuant to the Equal Credit Opportunity Act specifically provide that a creditor may take immigration status into account in evaluating a credit application. In the absence of an indication of Congressional or regulatory intent to equate citizenship requirements with consideration of national origin, the Court is of the opinion that alienage is not within the purview of the Act. See Espinoza v. Farah Manufacturing Co., Inc., 414 U.S. 86, 94 S.Ct. 334, 38 L.Ed.2d 287 (1973).
Nguyen v. Montgomery Ward & Co., 513 F. Supp. 1039, 1040 (N.D. Tex. 1981).
Those regulations still provide that immigration status may be considered. "(e) Permanent residency and immigration status. A creditor may inquire about the permanent residency and immigration status of an applicant or any other person in connection with a credit transaction." 12 C.F.R. § 1002.5.
The Fifth Circuit similarly held that the ECOA does not bar discrimination based on citizenship (alienage):
The reasoning of Espinoza controls this case. Discrimination purely on the basis of alienage does not violate the ECOA. The rationale of Espinoza does not suggest any grounds for distinguishing the federal credit anti-discrimination law from federal employment anti-discrimination law when the relevant statutes use almost identical language. Furthermore, we must assume Congress was aware of this important Supreme Court decision handed down several years before the amendments adding the EEOA-like language to the ECOA; the legislative admonition to follow federal employment law makes our decision easy.
Bhandari v. First Nat. Bank of Commerce, 808 F.2d 1082, 1101 (5th Cir.), on reh'g, 829 F.2d 1343 (5th Cir. 1987), cert. granted, judgment vacated, 492 U.S. 901, 109 S. Ct. 3207, 106 L. Ed. 2d 558 (1989), and opinion reinstated, 887 F.2d 609 (5th Cir. 1989).
And in a much more recent decision the 11th Cir. apparently felt that the issue was settled enough law that contention of violation of the ECOA on citizenship grounds was frivolous in an unpublished opinion:
We affirm the district court's judgment on Count I because Diaz–Verson's claim is frivolous. The ECOA prohibited the Bank from discriminating against Diaz–Verson "on the basis of race, color, religion, national origin, sex, or marital status or age." 15 U.S.C. § 1691(a)(1). The closest the complaint comes to alleging discrimination on the basis of any of these protected categories is the allegation, in Count I, that the "Plaintiff Diaz–Verson, Jr., was born in Cuba and is now a naturalized American citizen." This is simply not enough to make out a case of discrimination on account of "national origin."
Diaz-Verson v. Bank of Am., N.A., 159 F. App'x 71, 73 (11th Cir. 2005).
Bottom line here is that discrimination based on citizenship in lending decisions is not prohibited by the ECOA and I'm not aware of any other federal law that would make that illegal either, though if you know of one please do cite it, I'd like to see it. 
