The demand for these wild animals to be used as pets harm these animals directly. Not all of us can go down there and stop poaching on the frontlines (if you can, woah, you're awesome), but we can control what we consume and try to encourage others to consider the same.
Animal Agriculture harms these animals indirectly. This is something we, as individuals, can control.
When you consume animal products unnecessarily, you're creating a demand for something that takes a huge toll on the environment. Meat requires more farmland and resources than fruits, vegetables, beans, and nuts alone. This is because you need room for the farm animals to live and vast resources for the animal to be raised; think food, water, and places to dispose of blood, excrement, and the unconsumed.
This is why what humans eat have an effect on more than just the animal eaten. Please be mindful of the effects your actions take on the world around you as a whole with every action and purchase.
Don't just take it from me, I encourage you to do your own research on this subject. For you, the planet, and the animals (including our wild bird-friends).
If we stop the demand, we stop the harm. Mind you, no one is asking for perfection, but effort. Make a goal to do the least harm.