I've done a lot of googling and looking up, and maybe my game just isn't updating but- is it ONLY food items that increase Ariral rep? Or can other things too, like the ariral plushies? I left the red one in the treehouse to see but I don't want to run back and grab it if it's theirs now and it's "stealing" from them. 

Only food items increase Ariral rep, but when it happens, you can return their gun when they drop it outside for a huge reputation boost. They don't claim any items left at the treehouse, they only get mad for you stealing their stuff (posters and knives excluded, they are free for the taking.)

I've had rep increases from sleeping in the treehouse beds although they are much smaller than food and there is also a rep increase of about 15 if you can manage to take a picture of the ariral ship before it teleports away when the spam email saying "outside" happens.

Not only food. My rep increased when I brought them a table from tr_2. Maybe it was some kind of bug, I'm not sure. I just didn't want to leave food on their mattresses because it sinks into the texture a bit and you can't tell if it's gone or not.