There are a couple of problems with this. First, the Fourteenth Amendment doesn't have a whole hell of a lot to do with what current or past practices are, the notion of protected rights is that they exist independently of institutionalized practices and come prior to them. On a philosophical level ,it is irrelevant whether or not a practice has a long standing institutional history (in practice, of course, judges take institutional history into account, but this is irrelevant to the rationalization of a bill of rights distinct from public law).
Second, there is no particular way that marriage was understood from the beginnings of human societies. There is a vast array of marital practices that have existed at various points in time in response to various social and material pressures. The form that marriage takes is simply a cultural adaptation to these circumstances. One need go no further than Wikipedia for a lengthy list of types of marriage (same-sex marriage is listed separately). This list probably isn't exhaustive (though I didn't read the Wikipedia article in depth, so can't be sure), since I didn't notice marriage like practices that existed among transvestites in southeast Asia, to name just one instance. This kind of appeal to authority greatly annoys me, it relies on a combination of ignorance and certitude that doesn't withstand a 30 second web search. Even within the Bible, we read frequently of non-traditional practices such as levirate marriage and incestuous marriage. Any notion of "traditional" marriage is completely arbitrary taking both an arbitrary beginning point and an arbitrary end point for an institution that has been in constant flux and change throughout history.
As to the slippery slope argument, all that needs to be said is that everything mention involve either well understood risks which there is a strong public interest in preventing (incest) or present difficult institutional problems, like group marriage. This is not to even address the more extreme positions that I've seen mentioned (though not by Gottfried) such as pedastry or animal pairings which would conflict with other human rights notions such as consent or equality.
The second problem is that Gottfried presents human rights as significantly less stable than traditional moral guidelines. He states:
Whereas most of us in the same society up until a few decades ago could have agreed on what actions were right and wrong, human rights are more subject to change than traditional moral verities. Their validity depends on political and cultural winds; and it is foolish to believe that one can bridge the breakdown of moral or social consensus throughout the Western world by resorting to a new universal ethic based on “human rights” or “democratic values.” There are sharp and even growing differences in our society about fundamental behavioral questions, and appeals to supposedly universal rights language will not likely heal these divisions.This is wrong on several levels. First, traditional moral verities have no stability themselves, whenever confronted with novel social or economic circumstances societies always go through significant soul searching. To go back to marriage, we are well past the old European marriage pattern where women were expected to marry young and have sexual relationships solely with their married partner while men were expected to marry late after they had attained financial security to support a family but were able to be sexually promiscuous up until marriage (and in some places and time, after). The modern "traditional" marriage didn't emerge until the 19th century when industrialization and flight from the land meant that men were able to establish themselves by their early 20s, and often their teens, leading to equal expectations for both men and women to have sex only inside marriage.* In short, traditional moral verities only exist if an arbitrary point is taken, if looked at historically morality has always been fluid and subject to social pressure.
The second problem is that Gottfried seems to completely miss the point of human rights. The notion of human rights is the obvious outgrowth of the idea of natural rights encountering a world outside of the Christendom that it evolved within. The fact that other societies had vastly different notions of morality has to be taken into account by anyone who wanted to claim that there was a universal grounding for morality that could be applied to all men. Human rights is the natural consequence, it is asking what rights are truly universal and can cross cultures. Its apparent fluidity is a consequence of the short period of time that this cultural interaction has been occurring, the idea of natural rights took several centuries to evolve into a relatively fixed pattern in Europe. While technology is speeding this dialogue in the modern world we shouldn't expect it to happen overnight.
As for the notion that "most of us in the same society up until a few decades ago could have agreed on what actions were right and wrong," I see two problems. First, this is probably to a large degree the result of relatively few people participating in the conversation. While there was a broad consensus among American WASPs, I doubt that the same consensus existed among black sharecroppers in the south or among lower class migrant farm laborers. A second problem is that this is inherently culture bound; sure, within our society there may have been a broad consensus but this doesn't provide us with a way to discuss morality with Communist China, Shia Iran, or with the tribes of the Congolese interior. Human rights is an attempt to bridge this gap, retreating within our own culturally bound spheres simply avoids this question, not answers it.
Now it may be possible to argue that we should take a live and let live approach, regard morality as irreducibly culture bound, and not insist on any sort of moral universalism that applies to individuals regardless of their institutions but this isn't the argument being made here. Instead, it implies that there was something correct about how we did things and that attempting to deal with the moral complexity of a wider world is nothing but empty rhetoric. But Gottfried's approach offers us nothing to guide us in a complex, changing world and it fails to even notice the existence of the moral quandaries that human rights is trying to solve.
* I tend to see the breakdown of modern marriage to be almost solely caused by trying to retain the traditional conception of marriage in a world that does not have economic institutions to support this. The Victorian idea of marriage is rooted in a man having a lifetime job that is able to maintain a family without having to move or leave his local community. In a world where people will have 7 or more jobs in a lifetime, where matching your inherent aptitudes to employment almost always requires mobility, and where women are accorded equal status rather than dependency this type of marriage is an impediment to stable families. If we want stable families we need to develop marriage institutions and attitudes towards sex that embrace mobility, equality, and a long term of human capital development. No society has ever expected people to remain virginal into their late 20s or early 30s but that is the normal length of time for someone to obtain the stability to make marriage work. Greater worker protections and higher incomes for the lower skilled would help at the margins, but for the most part we can do little but come to terms with a world in which sufficient human capital to provide stability can't be developed until relatively late in life. This was the case for much of our past history, but stable marriages were only created by the subordination of women and their lack of equal rights. We can't have an expectation of young marriage (traditional marriage), an open economy, and equal rights for women. At least one of these things have to give and it looks like it is going to be young marriage.