One aspect of "The Universe leads, we can only follow" that I keep thinking about is how wish craft fits into it.
On the surface, that sentence seems to mean that Islanders believed in some sort of destiny created by the Universe. Or at least, a philosophy encouraging them to accept whatever comes their way in life. Yet the Islanders seemed to freely and often use wish craft*, something that, at its core, is about changing stuff in your life.
(*Siffrin notes this when praying to the Change God for the first time. "It's considered lazy to just ask for stuff here." Implying that it was a fact of life that you could, and should, just ask for stuff. There was (seemingly) no taboo about it. "Seemingly" because we need to keep in mind that Siffrin was cut off from his culture at a young age, so some nuance they might have learned about later in life was probably lost.)
Anyway, using wish craft to basically change your destiny daily while using "we can only follow" as a mantra feels a bit contradictory!
So my interpretation of this sentence kinda shifted overtime in my mind, and now I'm convinced it is precisely about wish craft, actually.
Wish craft is a manifestation of the Universe. If you ask a favor to the Universe, you can't contest Its answer. However unpredictable. However constraining. Furthermore, if the Universe decided of a way to solve your problem, then this answer has a meaning and you should seek to understand this meaning.
At least, a majority of Islanders probably believed so, as examplified by Siffrin and King trying to find meaning to the way the Universe answered their wish. Siffrin resenting It in act 5, King taking his new powers as an express order to enact his plan.
But like all religions, I like to think that it wasn't a monolith, and maybe some Islanders would take a less antropomorphised approach to wish craft, where the unpredictability is a matter of random chance and less about the Universe having a will. Either way, I think it still fits the mantra.
Whatever the Universe decided to provide, you have to live with it. Whether or not you believe It had a specific reason for giving you this specific solution.