We use Seventh Generation products and their Natural Baby Laundry Detergent. It is not tested on animals.
There was a consumer who was worried that their products are tested on animals, not by the company, but by a 3rd party (see link). However, Seventh Generation responded by saying that they use existing test data which was received when they licensed their products to another company. They didn't directly contribute or commissioned any of their own tests. (So it's as if the other companies wanted assurance of animal testing, and then provided test results to Seventh Generation for reference.)
You can also use natural laundry detergents from Etsy (just a random one I found). These have the benefit of being simple (no fragrances, additives, etc.) and are not necessarily more expensive to use. The downside, of course, is that if you're out - and didn't order more - you got to go get something else from the store!
You can also make your own laundry detergent. If done in bulk, it's not too much work or difficult. And saves a heck of a lot of money.