Here's a good discussion of rational basis review by the Supreme Court. It's not hard to see just how deferential to the legislature it is.
We many times have said . . . that rational-basis review in equal protection analysis "is not a license for courts to judge the wisdom, fairness, or logic of legislative choices." Nor does it authorize "the judiciary [to] sit as a superlegislature to judge the wisdom or desirability of legislative policy determinations made in areas that neither affect fundamental rights nor proceed along suspect lines." For these reasons, a classification neither involving fundamental rights nor proceeding along suspect lines is accorded a strong presumption of validity. Such a classification cannot run afoul of the Equal Protection Clause if there is a rational relationship between the disparity of treatment and some legitimate governmental purpose. Further, a legislature that creates these categories need not "actually articulate at any time the purpose or rationale supporting its classification." Instead, a classification "must be upheld against equal protection challenge if there is any reasonably conceivable state of facts that could provide a rational basis for the classification."
A State, moreover, has no obligation to produce evidence to sustain the rationality of a statutory classification. "[A] legislative choice is not subject to courtroom factfinding and may be based on rational speculation unsupported by evidence or empirical data." A statute is presumed constitutional, see supra, at 319, and "[t]he burden is on the one attacking the legislative arrangement to negative every conceivable basis which might support it," whether or not the basis has a foundation in the record. Finally, courts are compelled under rational-basis review to accept a legislature's generalizations even when there is an imperfect fit between means and ends. A classification does not fail rational-basis review because it "'is not made with mathematical nicety or because in practice it results in some inequality.'" "The problems of government are practical ones and may justify, if they do not require, rough accommodations-illogical, it may be, and unscientific." (internal citations omitted) Heller v. Doe, 509 U.S. 312, 319-320 (1992).
This is all very true...
However to make a definitive statement that rational basis review is the standard that will apply is unknown at this time, that's what the SCOTUS will have to determine. Those better at the law then I can surely make an argument (and have done so in cases that have already been reviewd and upheld by the 10th and 4th Circuit courts.
First, as your unsourced quote (presumably it is from a SCOTUS case) points out, rational basis is not the level of scruitiny applied when laws work to inhibit a fundamental right. The SCOTUS has repeatedly recognized that Civil Marriage is a fundamental right (Zablocki v. Redhail and Turner v. Safley and Loving v. VIrginia).
Second, the independent area of examination is "suspected lines". Starting with Romer v. Evans the court began to recognize that laws that target homosexuals were unconstitional not even surviving a rational basis examination.
Romer v. Evans
Amendment 2 fails, indeed defies, even this conventional inquiry. First, the amendment has the peculiar property of imposing a broad and undifferentiated disability on a single named group, an exceptional and, as we shall explain, invalid form of legislation. Second, its sheer breadth is so discontinuous with the reasons offered for it that the amendment seems inexplicable by anything but animus toward the class that it affects; it lacks a rational relationship to legitimate state interests.
Lawrence v. Texas
The second post-Bowers case of principal relevance is Romer v. Evans, 517 U.S. 620 (1996). There the Court struck down class-based legislation directed at homosexuals as a violation of the Equal Protection Clause. Romer invalidated an amendment to Colorado’s constitution which named as a solitary class persons who were homosexuals, lesbians, or bisexual either by “orientation, conduct, practices or relationships,” id., at 624 (internal quotation marks omitted), and deprived them of protection under state antidiscrimination laws. We concluded that the provision was “born of animosity toward the class of persons affected” and further that it had no rational relation to a legitimate governmental purpose. Id., at 634.
Windsor v. United States
The responsibility of the States for the regulation of domestic relations is an important indicator of the substantial societal impact the State’s classifications have in the daily lives and customs of its people. DOMA’s unusual deviation from the usual tradition of recognizing and accepting state definitions of marriage here operates to deprive same-sex couples of the benefits and responsibilities that come with the federal recognition of their marriages. This is strong evidence of a law having the purpose and effect of disapproval of that class. The avowed purpose and practical effect of the law here in question are to impose a disadvantage, a separate status, and so a stigma upon all who enter into same-sex marriages made lawful by the unquestioned authority of the States.
Romer, Governor of Colorado, et al. v. Evans et al., 517 U.S. 620 (1996).
LAWRENCE V. TEXAS
UNITED STATES v. WINDSOR | LII / Legal Information Institute
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The the first question the SCOTUS will have to answer: is marriage a fundamental right that applies to same-sex couples? Secondly, did the passage of laws that denied equal treatment under the law, which anyone will honestly recognize as starting after the Hawaii case in the early 90's, target same-sex couples along suspect lines.
The court has repeated said that Civil Marriage is a fundamental right - that could raise the bar above rational basis. Independently the courts have also found unconstitutional laws that target homosexuals for discrimination - that could also raise the bar above rational basis. Whether that would be heightened scrutiny (along the lines of gender) or strict scrutiny (along the lines of race and religion), we don't know yet.
Then of course they could use rational basis and point out that the law doesn't even meet that standard.
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