I have 2 properties in Joshua Tree, one has been listed for several months and the other listing is about to go live this coming week (we have done extensive renovations on each).
Currently, as Joshua Tree is in San Bernardino County, you have to register your STR at the county tax office and pay the 7% TOT quarterly (end of Jan, April, July, and October). You self-report your revenue and pay 7%, which, of course, is normal to pass on to your guests. I walked in to the county office and registered my property same day, and got the actual license (which must be posted in your home) in about a week.
Have not heard anything recent, but there has been word of an ordinance coming out in the city of Joshua Tree. The city council website has some info, but that website does not seem to be updated regularly. Ordinance from the city would be good, as regulation means it is allowed legally and would make it more difficult to ban it (although I don't think that is likely to ever happen).
You are probably aware of the climate -- Palm Springs (city proper), just passed an ordinance limiting the number of rentals you can have per year. Other low desert cities may pass regulations, but have yet to do so. 29 Palms just passed an ordinance allowing it, and part of the push was to join the economy created by STR's as the neighboring cities have already been taking advantage of it.
Joshua Tree is a different kind of city (different from neighboring Yucca Valley, which has more of a suburb feel and 29 Palms, which is a military town). JT is home to artists, musicians, and the people there are very protective of their town and its identity. They are opposed to big business, gated community developments, and the people will fight against any big company trying to open a store in town or doing large-scale real estate developments. Big hotels are never likely to come to JT. This creates a strong short-term rental opportunity, and the city seems to embrace STRs. However, you have to keep the small-town, community-pride feel. If neighbors, or people in town, see you as someone that is not from the area trying to build an STR empire, you will likely get brushback.
As I also do STRs in Orange County, CA -- comparitively, I view JT as relatively low-risk to ever losing the option to rent out my properties short-term. I try to stay involved in the community and talk to my neighbors (I don't live out there but do a lot of work on my house, so people see me often enough to think I'm a "local"). I also try to support local businesses as much as possible.
I watched the whole Anaheim STR ban go down over several months and actually watched several 3-4 hour council meetings in their entirety. The bad STR owners ruin it for everyone. STRs are a unique kind of real estate investment: a hybrid of a hospitality business and a single-family home. You have to run the business like a hotel (customer is always right, don't go cheap on stuff, communicate often with your guests, ensure their vacation is memorable). But you have to also realize you are a single-family home in a neighborhood, and you have responsibilities just like any other homeowner. Noise control, trash control, parking control, looking out for the welfare of your neighbors, being involved in the community, understanding unique local concerns (e.g. light ordinance in JT or the care of environment concerns in JT). It's not enough to just tell your guests, you have to have checks in place to make sure the noise, trash, and parking do not get out of hand.
I follow listings in certain neighborhoods in JT and have noticed that things are selling very quickly now, often cash offers (as they close within a week). Prices have appreciated a lot, and listings sell for around list. It's obvious what's going on, and I just hope the STR owners will not ruin it by treating it strictly as a business and forgetting about the community at large.