Sheer blinds make excellent window coverings that are pet friendly and pet proof. Pet hair and dander won't get caught in sheer blinds, and you can easily gather them off the floor and use hooks to pull them up so your animals won't be tempted to claw them or use them as a toilet. Also,sheer blinds can go right in the regular, everyday wash, so they are much easier to care for than you might imagine.
Old fashioned pull-down shades are making a comeback with pet owners. The reason is they don't attract pet hair, and they are also somewhat durable. The trick is to know how to use them. Most of the time, window treatments are damaged by animals who want to push them aside to peer outside. So, if you use your window shades and only pull them down about 3/4 of the way, your pet will still be able to look out the window, and won't be tempted to try to damage the shade.
A twist on the indoor window treatments that won't be too destroyed by pets is shutters. Shutters are most traditionally found outside windows on the exterior of the house. However, if you hang shutters on the inside of your window and secure them to the wall, you can close them with hooks, and you'll have a window treatment that your animals can't really chew up. You will have issues with these shutters if your pets chew wood, but if your pets are going to destroy wooden window treatments, they'll probably destroy anything you put there.