Is there any denomination that thinks the Rapture can be produced by human activity?
Ignoring the likelihood that there is some sort of us-four-and-no-more (very) "out there" somewhere who does, no. The heyday of eschatological speculation was 30-50 years ago (Hal Lindsey, Salem Kirban, and several others), with somewhat of a revival of such speculation 10-20 years ago with LaHaye's
Left Behind series of novels. It's a distinction I don't think TMN would notice or acknowledge, but the thinking of 60s-80s eschatology speculators was passive, seeing various events as signs the Rapture, Tribulation, and Second Coming were imminent. Not active, as in, "If we do X, Y, and Z, can can make the Rapture happen sooner."
Further, their thinking was to warn people as to what was coming, in the hope that people would become believers (and thus escaping horrible things through the Rapture), not hoping to somehow hasten the End, which would result in fewer becoming believers and being Raptured out of the horrible last 7 years of Tribulation. There is a sort of
Blood Libel (metaphor alert) out therein some Jewish circles and, evidently, some Prog circles that Christians who believe in some version of Dispensational eschatology look forward to the slaughter such eschatologies envision happening in the final years before Jesus' Second Coming. Having been in such circles for over 4 decades, I can say from what I've seen that this is libelously false.
TMN is not speaking of any real Christians he's met or whose writings he's perused. He's concocted in his malignant imagination what he imagines Christians should be like, and therefore are. It is those bogeyish figments of his malignant imagination that he condemns. What compounds the sadness of what he has made himself in this respect is that few, if any, DU-folk know any better. I don't wander in there very often, but I doubt any who know better care to speak up about reality, leaving other DU-folk to think TMN knows what he is talking about.
I don't mind at all being criticized for real faults, but TMN's rants are

grade.