Depends on your definition of "meaningful". But if we stick to things with measurable in-game consequences, rather than the personal satisfaction of players who find meaning in supporting one faction or another...Which leaves only one real question: Does it matter in any meaningful way who controls this, or any other system?
I'm going to guess "No".
...on an individual station level, changes in faction ownership can open or close certain services (black market, interstellar factors, material traders) on a semi-permanent basis. The government type of the station controller also affects which modules are offered in outfitting, and which goods are legal in the market (which can cause rare goods to semi-permanently vanish from the game [1]).
...on a broader level, there are advantages and disadvantages to the independent trader, pirate or bounty hunter from having all stations in a region controlled by different groups or having them all controlled by a single faction. For example:
- all stations controlled by the same faction will share a BGS state and therefore a set of trade price effects. This makes profitable trading between them usually less effective and can lead to regional supply shortages
- all systems controlled by the same faction share a jurisdiction (which in many cases is part of a superpower), meaning that the impact of crimes committed is more substantial
- different configurations of factions, especially as they sprawl across many systems, are more or less vulnerable to the significant economic states of Lockdown, Civil Unrest, Famine and Outbreak which provide major opportunities ... or not ... to various professions. Similarly this can affect mission availability a bit.
...government types in most of the bubble also affect the ease of Powerplay control of particular spheres, which even if you don't directly care who "wins" Powerplay this week ... most of the Powerplay spheres further apply global effects to trade prices and/or service availability.
...there are feedback effects (in that you don't have to care who owns a station for the fact that other people *do* to affect you) on things like CG placement, Thargoid raids, etc. Occasionally these - e.g. Lave - get big enough to be more obviously noticeable.
Of course, the bubble is large enough that one can avoid having to care in the slightest who owns any particular station or set of systems - if the local configuration is unfavourable, there will be plenty of other places which are better, and if one of those becomes unfavourable later it's always possible to move on again. That's not the same as the local changes being unimportant, though.
[1] If LRN had picked "Theocracy" as their government type it'd make the current cycle of complaint threads look mild