I was worrying that it might matter less than one would think. The Paean points out that facilities aren't really locked by faction at all. Some are better suited for certain social engineering choices, but even that's iffy.
Recycling tanks are a relatively benign and early example, mostly scary for how omnipresent they tend to become. A cultural taboo gets tossed out (well, recycled) almost immediately upon Planetfall, in order to survive. I like how it hints at the further stages of... change that humanity will undergo.
A lot of faction builds can't nerve staple (entire bases) or rely too heavily on police, and yet anyone can build a
genejack factory with the proper technology.
Still, Lal's quote for the Recreation Commons indicates that the same "facility" might look very different in different factions. Why wouldn't a Morganite take a loan against their body? Or a Gaian return to the circle of life? One commenter suggested that Hive citizens might enter the tanks alive, but I wonder if they're the only ones.
On a lighter note, something I didn't really understand is how little manual labor is likely necessary from the Centaurans.
Industrial Automation and similar techs describe an economy based on robots and telepresence. Human lives are too rare and fragile to be wasted moving boxes in this hostile environment. Eventually they go full super-saiyan/transcendent, but this mechanized industrial base happens surprisingly early on. It's an interesting rule of the setting that they quickly discover ways to conveniently store and utilize incredible amounts of energy, yet the lack of fossil fuels makes powered flight (and chemically-explosive weapons) impractical.
The Paean for the Genejack factory touched on the implications of that. Genejacks aren't dumb zombies that cart metal ore around. They're perfectly intelligent - perhaps even optimized - they simply lack any personal ambition. Chilling stuff.
I kinda wish the Fundamentalist social engineering wasn't so mechanically bad, because it would seems to fit the Gaians well thematically. Not that Democracy is antithetical to them, but... yeah. I definitely spent a lot of time romanticizing them.