I'm not into plants, but I'll have to ask my mom, because she is a nutcase about them/gardening in-general (she has an actual, wooden greenhouse that she bought as a kit, it's nuts, it looks like a cabin attached to the side of their house)...Her house has always been full of house plants since I was a little kid, and Jagger doesn't seem to bother them, and I'm sure they are bird-safe knowing my mom...But I have no idea what they are, lol..I'll find out...
****What I can say is that the only plants that I have in my house all over the place are different Succulents, and none of the birds have ever even noticed them or bothered them one bit (they are all fully-flighted and all over the house every day)...I think it's because they don't really look like "plants" at all, and they just don't bother them or go near them...And they are all okay to eat, I don't have any toxic ones, most of the chicks and hens, the jovibara, and the smaller, more colorful warm-climate succulent species are fine to eat and people actually cook with them, so you might try that...