I really, really disagree with Jeff Atwood here. Jeff has interpreted "learn to code" with "become a programmer". They're not the same thing. I don't think that is what this meme is about at all. Programming is logical thinking in practise. Programming is breaking a problem set down, thinking step by step through it, thinking of edge cases, and making it work. There is nothing wrong with Jeff's BASIC example, if that…
I don't understand the distinction you raise in the first paragraph. Coding is programming. Just because everyone can divide doesn't mean everyone is trying to be a mathematician, but I think everyone should (at least have the opportunity to) learn long division. Programming may not be the fourth "R", but maybe "Research" is!
However, given the current state of the world, where many things are in one way or another controlled by software. It would be a good idea to have a skill related to coding, just to know if something is possible with code. And understand that it is not just magic under the hood.