Can someone "explain" what the fifthist church is?
It's a multifaceted group of astrological star cultists manifesting in different parts of the globe in the form of celebrity fraternities, rock bands, churches, etc.. Occasionally they're anomalous, but mostly they just worship a vague goal of physical and psychological cosmic transcendence. They're probably one of the hardest groups to really get a concrete handle on, so don't fret if you're still completely lost after looking over some of their stuff. That's what makes them fun and creepy.
What are its goals?
They frequently seek to recruit new members, and their beliefs can be loosely described as a pursuit of transcendence, but to be honest, they really aren't rational or coheisive enough to have anything that can be described as a set of goals. They just sort of do things because the voices tell them to.
one of SunnyClockwork's goi ball comics sums it up pretty well:
For me, the theme of fifthism is religiousity without any core coherent human theology. The trappings are familiar, but the center is something alien.