Please check this out: How Scared Should You Be of Off-Gassing? #greenliving
https://www.custommade.com/blog/off-gassing/
Since we don't live in a perfect world, we can't avoid all harmful chemicals but we can do our best not to add more to our environments
Almost all tile here with animals and heavy floor traffic it is the only sensible solution for us. We did put a Bamboo runner in the bathroom for stepping onto out of the tub and shower. I suppose if you are set on carpet you could insist they lay it out in your yard before installing? You can get both tile and wood with nonslip texture.
I am 90. Even with carpet I fractured my left femur last year. Throw rugs are out especially in the bathroom and halls. Area rugs would need to be anchored. But PLEASE for your health AND that of your birds use only safe, safe, safe floor coverings.