We had 5 cats for years and one was especially notorious for tasting plants!! I got a spray bottle and filled it with water to spray her when she got near any of the plants but it got to the point where she thought it was a game ... she'd turn to take a bite out of a plant, then turn back and look at me and when I'd point the spray bottle it in her direction she would squint her eyes, wait for the spray and then run ... 2 minutes later she was back again, meowing for me to spritz her! It was a constant struggle with that one; I had to watch her like a hawk all the time! One of the other cats only liked to eat the African Violets but I was able to put them up on higher shelves where she didn't attempt to climb.
So many plants are toxic to dogs and cats; it's always best to be safe rather than sorry. I really like that idea of using an old bird cage to cover the plant(s)!