Rather than responding individually to a bunch of posts, I'm just gonna make a post that VERY basically describes some of the legal issues here. Hopefully it provides a little insight that helps to inform the conversation. It is important to know that these are very involved, very nuanced legal issues with many possible permutations and intertwined variables. So, rather than trying to be perfectly and technically accurate (which would be beyond my capability anyway, and would take 20 pages which no one would read), I'm just gonna describe a very basic model and try to paint the general legal landscape. It won't be precisely technically accurate, and it would be easy to point out where it isn't - so I just want to acknowledge that up front - the general idea is what I'm trying to convey here.
First, when it comes to deciding which government policies are acceptable, which are 'Constitutional', the crux of the issue is determining which judicial review standard is to be applied. There are basically three, though they are referred to by different names, and sometimes hybrids of these are applied, and to some extent they overlap:
(1) Strict scrutiny - if this standard is applied, then the law or policy in question must be 'narrowly tailored' to serve a 'compelling' government interest. Furthermore, there can't have been a less intrusive way to pursue that compelling government interest. Strict scrutiny presents a very high legal standard, and it will usually mean that a law is Unconstitutional. Under it, basically there is a presumption that the policy doesn't pass muster, and it is up to the state to demonstrate why it does.
(2) Rational basis review, sometimes called ordinary scrutiny - if this standard is applied, the law or policy in question need only 'reasonably' relate to a 'legitimate' government interest. The standard basically presumes that a policy does past muster, and it is up to the challenger to demonstrate why it doesn't. It presents a very low standard, and usually means that a law is Constitutional.
(3) Intermediate scrutiny, sometimes called heightened scrutiny - this standard is somewhere between the other two. When this standard is applied, the law or policy in question must 'substantially' relate to an 'important' government interest.
Now obviously, some vagueness still remains. But, I think it is fair to say that, if strict scrutiny were to be applied, then most laws that unconditionally prohibit same-sex marriages would fall. I think it is also fair to say that, if ordinary scrutiny were to be applied, those laws would be upheld. So, the question really becomes, how is the level or scrutiny that is to be applied determined?
Well, rational basis review would be the base level that is applied by default. However, there are conditions which have legally been found to dictate higher levels of scrutiny.
If a law impinges a fundamental right, as identified by the Supreme Court, then generally, strict scrutiny is to be applied. For instance, if the government were to make a law that limited the right to free speech, then that law would be subject to strict scrutiny - and the government would have to have a very good reason to have the law, it would have to be narrowly written so that it only restricted activity to the extent that it had to, and there would have to have been no other, less restrictive, way to accomplish the same goal. As such, there are some laws which abridge free speech that are Constitutional, but most such hypothetical laws would not be.
It is important to note that, per the Loving case which Vrai cited earlier, and others that preceded it, the right to marry is considered a fundamental right by the U.S. Supreme Court. The question is, does that just mean heterosexual marriage is a fundamental right, or is homosexual marriage also a fundamental right? As it stands now, I would say it is only the former - and I don't think that is likely to change anytime soon. I believe that for various reasons relating to the standards the high Court has established for determining whether or not something is a fundamental right, which I won't get lost in here.
Now, if a 'right' is protected for this reason - that is to say, because it is a fundamental right, then we refer to that as 'substantive due process' - which follows from the Due Process Clause of the Fourteenth Amendment. So, if someone was using this avenue to seek relief from a court, we might say they are making a substantive due process claim. It would also be possible to make a procedural due process claim, but I don't think that would be as relevant to this conversation, and I'm not going to explore it for now.
Additionally, a law can be subject to a higher scrutiny standard because it classifies people - that is to say, it treats different people differently on the basis of some immutable characteristic. Within the law, we have the concept of 'suspect class' - basis on which people might be classified, and discriminated against. The courts have identified certain suspect classifications, where the use of those classifications within a law, subjects that law to a higher level of scrutiny. This too is not an exact science, as there can be different degrees of suspect classes, and consequently, different implications for which level of scrutiny is applied. Race and religion for instance, are very clear suspect classifications. Laws which discriminate on those basis are generally going to be subject to strict scrutiny, and as such, are going to be Unconstitutional. To some extent, sex is considered a suspect classification, and legal classifications based on it are subjected to higher scrutiny.
As it is, sexual orientation - or as Justice Scalia likes to refer to it, sexual proclivity - has not generally been regarded as a suspect classification. Though, I believe Justice O'Connor almost started to make the argument for treating it as such in her concurring (not majority) opinion in Lawrence v Texas (2003). It should also be noted that, legislatures can define a suspect class should they choose to - or, courts can define a suspect class in contravention with legislative measures.
Basically, regardless of whether or not there is a fundamental right in play, a law can not discriminate for invidious, arbitrary or irrational reasons. When the basis for discrimination is a recognized suspect classification, then the law is generally presumed to discriminate for those reasons (though there are obviously exceptions, and it is still possible that the law is Constitutional). Now, challenges made under this rational are generally referred to as equal protection challenges. They are made pursuant to the Equal Protection Clause of the Fourteenth Amendment. Very often, challengers make both arguments - that there is a substantive due process violation, and an equal protection violation - that a fundamental right is implicated and that there is discrimination which doesn't comport with legitimate reasons. Just to complete the circle, the Privileges and Immunities Clause is mostly irrelevant - as I've explained at length in other places.
There are also other reasons that a law might be subject to a higher scrutiny standard, but I don't think they are relevant to this conversation.
It is my belief that the more relevant legal issue here is equal protection, at least that is the one that will matter legally in the near term. So, the real question is, is homosexuality a suspect class? As of now, it generally is not. Legislatures can start to it as such (which some may have), or courts can start to consider it as such. As far as the Supreme Court goes, I have little doubt that it will eventually start considering sexual orientation a suspect classification, but I don't think that will happen tomorrow.