Our society runs on code sure, but it also runs on alloys and we don't expect a well-educated person to know industrial metallurgy either you know? It certainly makes sense to teach some models of computation, computers aren't magic and shouldn't be thought of that way. But it's fine to treat programming as a highly specialized technical domain like actuary or crop science or eye surgery or welding or whatever. Plenty of important useful concrete skills are not taught except to people expecting to use them professionally.
Anecdotally though I know a lot more creative and humanities people who can code than I do programmers who can dance or write a poem. The self-identity of "computer people" has long been as an aggrieved, besieged outgroup. To whatever extent we are alien I think we chose that for ourselves. We can change it but we shouldn't start by blaming anyone else for it.