You can find info about this product by calling up the msds; and the environmental working group (EWG) has more stuff about ingredient safety.
The two preservatives are sensitizers and associated with allergic reactions. If you have allergies or skin sensitivities in your family you might be more careful when using this. Otherwise, the product in general is less concerning as a potential environmental pollutant than a strong disinfectant quaternary ammonium compounds.
With any product that has a smell, the perfume or some of the cleaning compounds can be bad for a tiny bird to breathe. It seems to me that this product is dependent on the actions of essential oils in addition to the surfactants in order to clean and smell nice. Those odors could be a problem for birds or sensitive people.
That being said, I think if you use this product with good ventilation it should be ok. I mean, even vinegar or bleach has a strong scent and is irritating to lungs. Any cleaner has risks.
This product is labeled safe for use around children and pets. Of course, you don’t want to get it in anyones eyes or on your skin. You do want to use plenty of fresh air. But I agree with the previous poster that the preservatives are concerning because they’d leave some residue behind. I notice they can’t be used in cosmetics. So I’d be reluctant to use this product to clean things my bird would be in contact with. I DO notice you’re supposed to rinse and wipe clean, but I wouldn’t want to use this on anything that isn’t hard and non porous.