Rabbits love non-native plants since they are often more lush and succulent tasting than native plants. Native plants are adapted to the desert climate and have learned survival techniques that go beyond drought tolerance.
Cactus -- such as sahuaro, ocotillo, cholla and prickly pear -- deters rabbits with their thorns. Young prickly pear cactus, however, are sometimes nibbled on when rabbits are very hungry but will survive. Rabbits also will leave most desert shrubs alone that taste bad, including jojoba, brittlebush and creosote, all hardy in Sunset zones 12 and 13. They do not bother most acacias because of their thorns -- including whitethorn and catclaw, both hardy in Sunset zones 10, 12 and 13.
Other native desert shrubs rabbits seem to ignore are hoary mint (Poliomintha incana) and Mexican oregano (Poliomintha longiflora) since the leaves are very pungent. These plants are hardy in Sunset zones 10, 12 and 13.
Rabbits usually won't eat non-native plants that taste really bad, but be forewarned that sometimes a dozen or more will taste a plant, causing a lot of damage, even though they don't actually eat it.
Non-native plants that rabbits don't like include rosemary and lantana species. Rosemary is probably too strong for them, and bush lantana (Lantana camara) has poisonous berries. Both of these plants are hardy in Sunset zones 10, 12 and 13. Oleanders are also poisonous, so rabbits won't eat them, and they are hardy in zones 12 and 13. A desert favorite for humans, red salvia (Salvia greggi) also seems to be ignored by rabbits, probably because of its bad flavor.
If you have just set out native plants, many times rabbits will eat them at first, only to later lose interest. It is worth the price of a roll of chicken wire to build cages for newly planted plants just to be safe. After the first year, you can most likely successfully remove the cages and find the rabbits will leave the plants alone.
Rabbits will often eat the bark off of young trees. Therefore, it is a good idea to protect the trunks with either fencing or by wrapping a piece of shade cloth fabric around the trunk for a year or two. Once the trees develop a tougher bark, rabbits will leave them alone.