It’s not clear that current Tesla models possess the hardware to be compliant with AirPlay. As has been pointed out above, Elon did suggest that screen mirroring was on the horizon nearly two years ago, something that was reiterated to me when I picked up my car in August 2015.
But how would that work? It’s doubtful that Apple would produce the API’s to enable this technology with touch screen input.
One possibility that is maybe more technically feasible is if the screen mirroring was pushed via the Tesla app. You run the app on your phone and an interface is shown on the center console that controls the app. It’s not ideal and third parties would have to work with Tesla to make it work but it wouldn’t be reliant on Apple or Google to produce the framework necessary to support this feature.
It turns out this type of technology is already being developed by Abalta called WebLink. It was demoed at CES with Waze announcing support and uses HTML5 modules to mirror the phone. Kenwood demoed a unit with the technology. Here’s a video of how this type of thing works.