Axolotls are illegal in many areas because of their ability to interbreed with native species. In New Jersey, they could breed with Tiger salamanders, which are endangered. In California, they could interbreed with California Tigers, which are federally endangered. Often, these hybrids are better able to survive than either parent species (Hybrid Vigor theory). If the hybrids can outcompete the parent species (one of which is endangered), then the parents are toast.
But don't let it discourage you from keeping caudates! There are many species which are just as cool. I would personally recommend Pleurodeles waltl. They're permanently aquatic, they're kind of funny looking, they're great eaters, they are very comedic, and generally make good pets.