Lavey inherited Crowleys penchant for *shocking the rubes* and eccentricity(as did all forms of LHP religions today) but other than that thers is very little direct Crowley or Thelema influence in Laveys Satanism, Lavey actually mocked Crowley and Thelema as his satanism was and is explicitly LHP, whereas as Crowley and Thelema are RHP and about uniting with God/the divine. Thelema is technically RHP , but Crowley in his lifestyle and his views and by extension Thelema could be said to be kinda Middle Pillar path...slot of unification of opposites ideas, principles, values, and ritual practices. But yeah technically RHP, and Lavey didn't much like Crowley or Thelema.
Temple of Set/Setianism, has a little influence from Crowley/Thelema, but only a little. Less hostile to both than Lavey and his satanism are. Michael Aquino was an early member of the CoS but felt it was lacking and thus started the ToS and he and lavey(and his church)had a falling out, though Aquino still always maintained Lavey had an infernal mandate from Set to start the CoS, was in a sense chosen...though didn't fully and properly fulfill the mandate.
Luciferianism(modern/symbolic, and neo gnostic luciferianism at least) HIGHLY inspired and influenced by Crowley and Thelema...but also almost in equal measure by alot of other influences too. But certainly much moreso than Laveyan Satanism or Aquinos Setianism were/are. Neo gnostic luciferianism is also heavily inspired by a early 20th century Danish occultist named Carl William Hansen(pen name Ben Kadosh). Luciferianism is particularly eclectic and varied in its influences and inspirations.
There are several other forms of satanism and various subsects, some more influenced and inspired by Crowley and Thelema, some less so(most to one degree or another though), then there is chaotism...which has LHP and RHP variants...and middle pillar...sons forms of which and many followers/practicioners very influenced by Crowley and Thelema, some less so(Chaotism is particularly influenced by Austin Osman Spare, Peter Carroll and others though).
Crowley and Thelema are a interesting thing.
He and it basically became the Christ figure or the new replacement of Judao/christianity. As those two kinda influenced islam, sikhism, and a host of others.
Crowley and Thelema became that for the modern era and the future...inspiring and influenced pretty much every modern occult and neo pagan religion both RHP and LHP. Even Wicca was directly influenced by Crowley and Thelema as its main founder Gerald Gardner was a student of Crowleys and I believe directly studied under him and had a little correspondence with him. He directly took from Thelema many of his wiccan beliefs...including the Wiccan Rede which is basically a more succinct, simplistic, rehash of Crowleys Thelemite dictum do what though wilt whole of law...love is law love under will...every man and woman is a star(in wicca shortened to *an it harm none do what though wilt*)
Well Crowley/Thelema as well as Madame Helena Blavatsky and her religion/philosophy Theosophy(which particularly inspired and influenced most modern new age religions and spiritualism). These two have as much shared influence and inspiration acrossed the board on a large number of new modern religions that are becoming the major leading religio-spiritual-philosophical trends of the coming future centuries.
Just as Judaism influenced Christianity which both of these did islam and islam...along with hinduism inspired Sikhism. Which are most of the world's biggest religions(not counting the far eastern ones of course...buddhism, taoism, confucianism. But interestingly there is a hypothesis...or opinion that in Yeshuas/christ's years between age 12 and his early 30s when he began his ministry...about which the gospels say nothing of his life, that he travelled and learned the mysteries or mystery school traditions ideas from adepts of them...including and particularly Buddhism from Buddhist adepts...hence Buddhism heavily influenced Christianity as judaism did, and hence vicariously later islam and sikhism, Alot if cross breeding of ideas and influences...anyways sorry gettingba little off topic here)...and Blavatsky/Theosophy and Crowley/Thelema are pretty much the modern equivalents of this...the founders of a new breed of future religions that will influence many religions to come(and in fact...already have. Theosophy primarily new age and spiritualist ones, but Crowley/Thelema many occult and neo pagan ones...both RHP and LHP).
