So, I don't know if people remember the early 2000s, but it wasn't a terribly great time to be a programmer. All the jobs were going out to India. However, I learned a very important lesson. You have to be competitive. If you were someone who couldn't see past cobol, you did become obsolete. While programmers in India are still relatively less expensive than their counterparts in the US, top programmers are still sought after and make significantly more than the rest.
Sure the barrier to entry is "low", but it isn't that low. I think one of the main problem is, calling someone a programmer is an extremely "broad" term. I know some who can barely string together a few lines of PHP code and other who design and build complex systems which run the world and improve people's lives. If you're a programmer who just "codes" HTML, which you learned over one weekend and haven't take the time to improve your craft, sure you may be working now, but you're likely to get wiped out easily since the barrier to entry into your line of work would be very low.
In a sense the OP is right in that programmers shouldn't be complacent. I know a lot of C coders who have serious BS ego issues and refuse to do anything but C and then complain that they can't find work after being laid off.
BUT, I'm not shivering in my boots due to Stripe and Wordpress. Any programmer knows there's a bunch of crap that's tedious work which can be automated away. The good ones automate them and improve their craft and focus their energies on building better systems. I think that even with Wordpress, Stripe etc, there's a lot of room form improvements in the way we develop.
I recall spending days getting a dialog box UI just right in MFC. I thought it was stupid then and after using C#, never used MFC to build a dialog box ever again. Result wasn't that I'm out of a job. I actually have been able to produce a lot more. Programmers are in ever more demand than before. Sure the field will probably get tapped at some point, but to say it's going to be due to "automation" which has been a staple in our profession since the very beginning is simply inane.
Going with the autoworkers analogy, there are people who turn wrenches and people who figure out six sigma. If you're doing something as simple as turning a wrench, sure, you will get easily replaced by robots. But if you're innovative and competitive, you'll be significantly harder to replace and you can probably find applications for your skills in many more places. There are certain skills you just can't automate away so easily.
I would argue that programmers/developers will have jobs long past even doctors (maybe). Repetitive tasks can easily be automated away, creativity and innovation on the other hand aren't quite as easy. (FYI, the reason all programming jobs aren't just in India is because the US still rocks when it comes to creativity and innovation, based on my own experiences as an employer/manager and in speaking with others in the same position who have programming staff worldwide)