I don't know, but I believed that FA are right-wing radicals.
Gaians and Unioners cannot be left-wing too much because dealing with corsairs. And recently only active unioner faction is Imperial Rebels, who are seems too be quite right-winged guys.
GC are doing more things about matriarchy than just pure femenism, at least I didn't noticed much left-wingish stuff in \W/~ or ~*~ rp. Yes we are talking about corruption of corporations and bla-bla, but from traditionalist point of view. Both factions want to install Imperial rule (with the empress sure thing), so kinda left/10. I can't say that GC are going full right wing in the same time, sometimes it's more like Xeno-like stuff, sometimes it not (because we dealing with quite a bit of foreign factions which is impossible with Xeno). And GC are tied with the outcasts, which means slave trade and other things that cannot be tolerated by left-wing faction in either way.