For years, I’ve used and reused twist ties that I got from products like bread. I used them to tie up or bundle cords, to close plastic bags of leftovers, and to throw away trash bags of shredded paper that can’t be recycled in my area.
Twist ties and toxic metal
Then I learned that some vets recommend not using twist ties around pets (here’s another one). This is because twist ties are made in China, and no one knows what metals are used in making them.
If your pet regularly chews on a twist tie that has lead, zinc or copper, that could endanger its health.
At the very least, it’s wise to keep twist ties away from pets and small children. I try to avoid buying products that use twist ties, and I never use them around the house anymore.

What to use instead
For most household uses, the most environmentally sound and non-toxic option is simply a rubber band. I keep rubber bands that come on product packaging.
Reusable cable ties are a great option for jobs where a rubber band won’t work. They have a tip next to the latch that you either push in or down to release the seal, but they’re otherwise just as impossible to open as a non-reusable cable tie.
Pets may eventually chew through them, but since they’ll be cinched tight, most animals won’t find it easy to get at them with their teeth or beaks at all. That link takes you to a package I ordered in 2011. It’s unfortunate they’re not recyclable, but I’ve re-used these for years without having to buy a new package.
Twine is another option. It’s non-toxic, although it’s not as reusable as rubber bands or cable ties. But that’s just because it’s hard to untie a good knot. One thing you can do is snip off the knot when you’re done using a particular piece. Then you can reuse that slightly smaller piece.