Games like D&D 3.5 and Pathfinder have an open license. I.E. you can do anything with the game data you'd like as long as you're not using any copyrighted graphics or content (adventure paths, etc). I can basically re-host all game info with no repercussions. Does Age of Rebellion have something like this? I'm interested in creating a web based character generator but don't want to spend the time working on it if it's simply going to be DMCA'd.
No, there is no open license, or free license, or published community use policy for Age of Rebellion, any of the Star Wars games, or any FFG games at all.
On the FFG legal page they say in short "this is all ours" and then go on to say:
For questions about non-commercial, non-professional use of our intellectual properties for recreational and hobby community oriented purposes (fan creations), please contact firstname.lastname@example.org
Naturally since the Star Wars games, like many of their games, are full of terms licensed from other folks (Disney/Lucasfilm in this case) there's very little legal way for them to say "Yes go for it."
They also do actively C&D and go after folks using their IP - just a month ago they caused netrunnerdb.com to get shut down.
You can try to chart the tricky waters of "game mechanics can't be copyrighted" and trademark and copyright yourself, and that might work with some properties, but Disney is one of the most aggressive trademark defenders on Earth. I'd suggest doing what they suggest, emailing their legal team and asking them yourself.