The hand-wringing is mostly an after-thought. The mention of Sodom and Gammhora seems to be an almost ironic, tongue-in-cheek slap that only the most paranoid fire-and-brimstone people would take seriously.
At least this writer is attempting to write in an honest way. I've seen a few writers try and conflate polyamory with incest and bestiality. But you know, here in the south, it's still legal to marry your cousin in many states!
Anyways I have a few thoughts about this that I don't want to post in the comments on that site:
1) Why are they all posting scripture to justify their disapproval? Polyamory is a personal choice. If they don't like it, they don't have to engage in it.
2) Legal marriage is a state institution, not a religious one. If they don't like it, they don't have to engage in it.