Just as there is "computerate" to describe those who show familiarity with, and ability to use computers, is there a word to describe the opposite, those who are computer illiterate?
The word I'm looking for includes both those who have access to computers but, for some reason, choose to keep away from them, and those who can read and write but have never seen a computer in their entire lives.
I'm not looking for insulting or pejorative terms.
Computer illiterate may be the best phrase for itself, but if something less potentially pejorative is wanted, perhaps novice would suffice, as in novice computer user or computer novice.
nov·ice noun \ˈnä-vəs\ : a person who has just started learning or doing something
: a new member of a religious group who is preparing to become a nun or a monk
Note: I included the second definition as a comment on the sensibilities involved in mastering various levels of information and computer technology.
computer-challenged is something that I already heard.
Alternately, consider computer neophyte.
neophyte: a person who is just starting out in a field of activity: a neophyte in snowboarding
Chances are if a person in a first world country is still computer illiterate at this stage it is because they are in some way afraid or intimidated by learning the technology so technophobe might fit the bill.
If it's an intentional avoidance of technology, Luddite may fit nicely. It broadly means one who is opposed to especially technological change. While it sometimes has a negative connotation, it can also be used quite lightly: "I'm such a Luddite I can't even turn on my computer without help."
It would seem logical that computer illiteracy is a trait of the cyberphobic
Cyberphobia is an irrational fear of or aversion to computers, specifically, the fear and/or inability to learn new technologies
digilliterate is something I've occasionally seen used.
Techno-peasants
People who would, truly, ‘rather use a pitchfork’.
https://www.urbandictionary.com/define.php?term=a%20techno-peasant
ps in some cases, I might be one of them.
I think just unmodified "illiterate" would work. No need to bandy about the bush. There is no more excuse these days for being computer illiterate than book illiterate.
In our project we call it digital illiterate.
In Dutch we have a word for it, by the way. Digibeet is a word play on digitaal (digital) and analfabeet (illiterate). In English the same would become digiterate. If you Google this word, you will find some references to it.
The construct 'non-computerate' has been used in this context in recent publications.
Keep in mind that 'computerate' is a 1980's attempt to popularise a contraction of 'computer-literate', which did not meet with overwhelming success (despite inclusion in the Collins English Dictionary).
When it comes to less synthetic options, one who is computer-illiterate by their own intent or desire might be described as a luddite. If they are instead willing users of computers, they might better be described as a novice or neophyte, but none of these terms are specific to computer literacy.
In IT jargon we sometime use lamer.
A lamer is widely understood to be the antithesis of a hacker. While a hacker strives to understand the mechanisms behind what he or she uses, even when such extended knowledge would have no practical value, a lamer only cares to learn the bare minimum necessary to operate the device in the way originally intended.
ADDED after the OP had added a limiting condition:
I'm not looking for insulting or pejorative terms.
I guess you will hardly find any single-word term (in general, not only in connection with the computer literacy) with a meaning "lack of something", especially "lack of knowledge", with non-negative connotation.
For the IT craft, any word meaning "computer illiterate" would be pejorative :) I cannot see any difference in connotation between lamer and technophobe or digital illiterate or luddite or cyberphobic.
