It's clearly the commandos. Couldn't possibly be anything else.
"...it isn't random but regular and constant among all of these types of sites. There is definitely an organized group at play here leading people to dead end results. My guess is that it is a religious group, who else could it be? This has happened to us more than a couple dozen times over the past year on multiple sites."
You know what the other possible common denominator is? You. You and whatever flawed screening system you use. Do you only contact people with certs? Do you exchange one or two messages and then ask to meet for coffee?
There are a host of things you can do in order to stop repeating this pattern over and over. Because it's not a religious group. It's not an organized movement at all. Instead, a large portion of people on any swinger/kink site are wannabes. They won't ever meet anyone, but the fantasy is enough and by not doing a very good job of screening, their needs are being satisfied while yours are not.