Not really, no, your union will only affect rankings (you'll get the same prizes if you're active enough, anyway), which foreteller shows up in certain scenes, and which union Ephemera and Skuld will belong to. Just pick the one you think is coolest, yoI'm still unsure which union to join. I'm leaning toward Vulpes or Unicornus. Does the union have any impact on how you experience the game? Decisions! DX
You can switch unions at any time, for a cost of 100 jewels and all of the lux you've earned for the week.