This might be a bit outside the box, and doesn't fit certain definitions of "right wing" (especially if one is using conservative Christianity as a baseline), but... how about Satanism?
IOTL, Satanism, as conceptualized by Anton LaVey in the '60s, can be summed up as a mix of Ayn Rand and Nietzsche with the theatrics of Aleister Crowley thrown on top. The philosophy underlying the Church of Satan, which LaVey called the "Left-Hand Path", was rooted in a rejection of egalitarianism, a celebration of egotism, and a vicious social Darwinism. It preaches that one should give kindness only to those who deserve it, show responsibility only to the responsible, get revenge on those who wronged you rather than turning the other cheek, and most importantly, be ferociously independent from any person or institution who might try to hold you back, churches and states alike. A lot of what LaVey was saying was pretty much a more extreme version of what many early libertarians and anarcho-capitalists were arguing.
Maybe, instead of LaVey, the founder of Satanism is a guy who's less of a showman and more interested in creating a lasting religious movement, meaning that this alt-Satanism doesn't get seen as a media oddity and a circus sideshow by holding Black Masses for reporters. It might not even be called Satanism; LaVey came up with that in order to draw that kind of attention to his movement and philosophy. IOTL, there
was a splinter group in the '70s called the Temple of Set that tried to do this (and is still around), but by that time Satanism's fifteen minutes were over and nobody cared. Here, these guys are running the show right from the start. Libertarians, feeling isolated amidst the neocons and Christian Right types who are taking over the GOP, gravitate to *Satanism after one or two high-profile libertarian leaders starts extolling its virtues. *Satanism enters the public consciousness not as a flash in the pan, but a right-wing/libertarian version of the New Age movement, a religion of proudly egotistical elitists. (Kinda like Objectivism.

)