Oh, mercy, this takes me back. I haven't thought about this book in years.
Did SISL inspire any cults: probably not. It was certainly adopted as a variety of scripture by some of the free lovin' communal experiments of the late 1960s-early 1970s. Why? Heinlein had gotten (no, I don't know why. There are still people who think that Starship Troopers is a significant political document) the reputation of a heavy thinking, rather right wing science-fiction writer through the 50s, and his sudden change when SISL was published in 1961 had a lot of power. Also, the time was ripe; SISL appeared to say that you could have all the sex you wanted, and God, and personal power; always a potent fantasy, but especially attractive at the time. I can remember talking to a seminarian (an Episcopal seminarian, that is) when Dune was published; he was completely, genuinely blown away by the idea of the Orange Catholic Bible and "ecumenical" scripture. Dune is a little later than SISL, but they grew in the same soil. Heinlein worked on SISL throughout the 1950s; I have long thought that the cultural boil over of the late-60s-early 70s was the culmination of a long, slow seethe under the surface of the 1950s. If SISL had an influence out of proportion to its merits, it's because SISL shared the same background.
What this reader says about the general cultural upheaval of the 60's and 70's I've always also thought applied to Church upheaval, too. We've talked about it before, but it bears rehashing. If all Catholics - lay, religious and ordained - were so impeccably educated in the preVII period, if all was peaceful and happy and contentment....how could things go so crazy, really in a matter of less than a decade? Perhaps all was not as we've been led to believe it was.