"Why Not Polygamy? A Question to Advocates of Gay Marriage"

A blogger about Christian theology questions people's opposition to secular full marriage equality:

I’m a person who, for better or worse, always looks at social trends (and trends in churches) and asks “Where does the logic of this lead?” I believe the logic driving the “gay marriage” movement leads inevitably to next steps in “liberation” from traditional marriage arrangements.

Whenever I mention this, however, many defenders of gay marriage argue that there is no massive call for legal polygamy or marriage between closely related persons. Or for abolition of government-regulated marriage. Be that as it may, my mind cannot help but wonder. If we could get in a time machine and go back to America (to leave aside for the moment other Western societies) fifty year ago (and I’m old enough to remember that time) we would find that almost nobody envisioned a coming day when persons of the same sex would be permitted to marry. A few lonely voices called for that occasionally but there was no “massive call” for legal gay marriage. It was only a dream of a few people who stayed mostly quiet about it except among themselves.

Now we see cable television programs about polygamous “marriages.” (I put “marriage” in scare quotes only to indicate these are not yet legally recognized in any state and are, so far as I can tell, still actually illegal such that the “husband” could be subject to prosecution as could the minister or other officiating person who performed the “weddings.”) These mostly exist among so-called “fundamentalist Mormons,” but that’s irrelevant to my point.

My question is not about a real or imaginary “massive call” for legalized polygamy; that may or may not happen in the future. (I suspect it will happen, but I can’t prove it.) My question is only about logic. (So please stick to that if you choose to respond.) And it is only to those who advocate legally-recognized gay marriage: What purely rational or [non-]religious-based reasons can be given for continuing to criminalize “plural marriage” or to deny marriage licenses to groups?

Now, just to stave off an avalanche or even a trickle of comments based on misunderstanding. I am not here discussing the ethics of gay marriage, so do not respond as if I were. I am only asking advocates of gay marriage how they would argue against, if at all, legal plural marriage. And by “plural marriage” here I am only talking about arrangements where all the parties to it are knowledgeable, free adults and where there is no abuse or coercion.

So, to be very specific, let me give a hypothetical example: A woman wants to be legally married to two men. [...] What ethical or legal arguments would you, who advocate and support gay marriage, give for continuing to prohibit plural marriage?

Then, let’s take it a step further. Image a biological brother and sister who wish to be legally married. One or both of them will undergo voluntary sterilization to avoid the possibility of having children (who might have serious birth defects as a result). They can prove to the government that they cannot have biological children, but they plan to adopt. To those who advocate and defend gay marriage, which is the same as saying redefine marriage from its traditional definition, what rational or purely [non-]religious arguments can you give for prohibiting such a marriage? If such a couple sues for a marriage license, what reasoning should a judge use (if at all) to deny their claim?