I've highlighted some great conservation groups in previous blog posts that have devoted a lot of time and passion to desert issues. Desert Protective Council, Basin and Range Watch, Western Lands Project, and Western Watersheds Project, for example. Another great group to check out is Desert Survivors. This non-profit has been around since 1981, advocating for desert conservation, but also organizing hiking and camping trips throughout the southwest.
They are also one of the many advocates trying to draw attention to the pitfalls of utility-scale solar on pristine public land, and the benefits of investing in distributed generation (e.g. rooftop solar) instead. Most recently they held an educational protest outside the headquarters of BrightSource Energy, which is building a 5.6 square miles solar facility that is expected to displace or kill hundreds of desert tortoises.
Shameless plug: You can become a member, support desert advocacy, receive the newsletter, and participate in Desert Survivor events that share and celebrate the peaceful beauty of our deserts.