I can't speak for them, but as a private pilot who has become friends with lots of folks who are not career airline pilots, I can tell you that the delusion among that group of folks is quite high that things like this aren't coming for their jobs -- and fast.
The self-flying use case is, at least from a technical standpoint, far more straightforward than self driving, and the cost incentives are pretty huge. Not to mention the fact that some of this tech has already made its way into private aircraft, with Garmin already having a production system in place where non-pilot passengers can simply push a button on an aircraft and it will completely autonomously find a suitable airport to divert to, communicate with ATC, and land -- even taking adverse weather into account.
There is also a lot of regulatory and tech work at the FAA to also try to ulitize drone-like systems to help operate aircraft. The reality is that the vast majority of time that a pilot is in a flight it is quite low-intensity work (if there is any work to do at all). The thought here is that remote pilots could control the machine (or assist a single pilot in the cockpit) during critical phases of flight. The advatange here, of course, is that a remote pilot could do many such flights over a short period of time, whereas the one on board is stuck to the one flight even in moments where he/she has absolutely nothing to do.
Whichever way you slice it, if you think there is some argument for fully or partially autonomous driving, all of those arguments are orders of magnitude more compelling in flying. Timing, of course, is the real question mark.