Unfortunately, this argument is usually confronted with an emotional argument of "how dare you compare same sex marriage to bestiality!" While emotionally satisfying, this argument essentially replicates the logic of same-sex marriage opponents. "I think this thing over here is beautiful and the other one over there is yucky! How can you even compare the two things?" While some moral decisions are inherently arbitrary, it would be nice to believe that this was more than simply a "battle of the guts" and that a counter-argument grounded in law to this challenge exists.
Besides, as anyone who has sat through a law class knows, it is the proper duty of lawyers in all cases to consider such arguments. This is the heart of the Socratic method. From torts to property to Constitutional Law to legislative process, the student will invariably be asked how to distinguish a statement made from a fairly horrible reductio ad absurdem. Besides, not all reductios are all that absurd. I am old enough to remember that in the 1980s, when the Gay Rights movement was pushing anti-discrimination laws and amendments, an argument of opponents was that amending the state laws or constitution to prohibit discrimination based on sexual orientation would obligate the state to reognize same sex marriages. Proponents of these amendments angrily denounced this conclusion with the same fervor as those rejecting the argumentum ad pedophilia do today. Nevertheless, such arguments were ultimately made with seriousness and accepted in some courts.
So here is an exceedingly brief legal answer to the question: "Why wouldn't a judicial decision in favor of same sex marriage prohibit laws outlawing bestiality, pederasty and refusal to recognize polygamy?"
The key flaw in the argument that a judicial decision prohibiting a state from limiting marriage to one man and one woman must automatically strip the state of any grounds for restricting marriage (or sexual behavior) is that it assumes such a judicial opinion requires an "anything goes" approach. In law, however, the basis for a judicial decision matters. Even if we take the most expansive judicial basis for prohibiting limitation of traditional marriage to one man and one woman -- the idea that the state has no rational basis for such an exclusion (a premise I have previously argued against in some contexts, but which carried the day in Massachusetts and has some modest support in Lawrence v. TX).
This is the strongest rationale for the "pedophile argument." If incentive to procreation, the historic limitation of marriage, and the moral judgement of a state legislature and/or a majority of the electorate do not provide a rationale basis for limiting marriage in the case of same sex couples, what remains for bestiality, et al.?
First, we must note that we have a conflation of two arguments. As of today, states may still chose not to recognize same sex marriage, but under Lawrence v. TX they may not criminalize same sex . . . sex. Clearly the ability to criminalize the sex act (what is at issue in pederasty and bestiality) is different from recognition of marriage.
So why didn't Lawrence v. TX annul the anti-pederasty and anti-bestiality laws? Because these laws have a separate rational basis beyond the restriction of personal morality. It is well established that the state has an interest in preventing both cruelty to animals and cruelty to children. New York v. Ferber. In the case of minors and of children the state stands in parens patria and has a unique recognized interest in protecting these classes of individuals because they intrinsically cannot protect themselves. It is equally well-established that this right on the part of the state supersedes the right on the part of the parent, or the right on the part owner of an animal, in certain circumstances. See, e.g., New York v. Ferber, 458 U.S. 747 (1982) (state's unique interest in preventing cruelty to children justifies prohibition on trafficking in child pornography). Cf. United States v. Stevens, 130 S. Ct. 1577 (2010) (general interest in preventing cruelty to animals not sufficient to outlaw trafficking in videos depicting cruelty to animals without evidence that trafficker actually engaged in cruelty by producing films).
These interests remain, and provide a rational basis for criminalizing both bestiality and pederasty, The state is well within its rights to determine that a child below a certain age cannot knowingly consent to sexual acts, and that requiring a child to participate in sexual acts (even when 'consensual') is inherently damaging to the child. While there is considerable diversity among states as to what constitutes an appropriate age of consent, and whether parents may make an independent assessment that a child is sufficiently mature to consent at a younger age (for those states that permit marriage at a younger age with parental consent than without), this is precisely the kind of individualized -- and therefore of necessity containing some level of arbitrariness -- judgement permitted to the state under rational basis.
A similar, if not identical, interest obtains in limits on incest and consanguinity. The state is entitled to consider that if close relatives could regard each other as potential sexual partners, it increases the likelihood of abuse. Close relatives are uniquely situated to engage in child abuse. Criminalizing such unions even between consenting adults provides additional safeguards necessary to protect children. Further, although the medical evidence for genetic diseases (which place a financial burden on the state and society generally) is somewhat attenuated, and although the state (under the rationale basis standard favorable to same sex marriage) is not allowed to consider procreation the purpose of marriage, the state is certainly entitled to observe that the plan to conceive children is often a motivation of marriage and that prohibiting marriage at what it considers a suitable degree of consanguinity is rationally calculated to discourage children through incestuous relationships.
We now come to whether a state can either criminalize, or withhold recognition of, polygamy. I have to say that I think under Lawrence it is extremely difficult for a state to criminalize polygamy in the sense of a bunch of people living together in a family unit -- since it is nobody's business under Lawrence who is bedding who (for the same reason, I suspect laws criminalizing adultery that are still on the books in many states are also unenforceable).
The harder question is justifying a refusal of the state to recognize formally various forms of group marriage. The difficulty here is that while the courts that have gone with rational basis test have told us what the purpose of recognizing marriage is not (to encourage procreation), it has not told us what the purpose of marriage actually is. Unlike incestuous relationships, there is no body of work providing us with any evidence that group marriage is somehow harmful to raising children or leads to any kind of abuse. To the contrary, group marriage (at least of the kind involving one man and multiple women) has a significantly greater claim to traditional practice and acceptance than same sex marriage had at the time the State of MA concluded that MA had no rational reason to refuse to recognize same sex marriage.
There are various economic aspects that could be raised. The burden on the state and on private providers of marital benefits would increase significantly in a polygamous situation. But the Goodridge court rejected the "financial burdens" argument. Nevertheless, the matter of scope and degree is significant (the addition of same sex couples to those eligible for rights is negligible compared to overall population growth, by contrast, group marriage could require significant expansion of benefits to a single set of recipients). Such problems could, of course, be overcome with a phase in rather than with a ban.
The best argument for favoring limiting marriage to two people is that the state has the right, under a rational basis test, to chose the best method of furthering whatever it is that marriage apparently furthers when granted by Massachusetts (family stability? conservation of wealth for children?) This is somewhat easier for those states like New York that rejected the argument under rational basis -- since the state is allowed to chose its preferred method of promoting procreation among all possible aspects.
But I confess I find it hard to articulate a reason why in Massachusetts a man legally married to several women in, say, Saudi Arabia is not entitled to have the validity of those marriages recognized in MA. Nor am I sure on what grounds the state of MA could deny me a second marriage licenses if I decided I were spharadi and Becky approved of my taking a second wife. Has there been any such case in MA?