Happy new year! So I was reading "Meiji no Tōkyō-go" 明治の東京語 ("Tokyo dialect in [the] Meiji [period]"), an essay by Kaburagi Kiyokata 鏑木清方 in his recently reprinted Zuihitsu shū: Meiji no Tōkyō 随筆集　明治の東京 ("Essays: Tokyo in [the] Meiji [period]"), when I came upon this:

読まん同士、書かん同士
こう字にかけば解りやすい。年齢のゆかない女中など二人以上で留守番でもさせる時「何しろよまんどし、かかんどしだから」といった工合。

Yoman doshi, kakan doshi
Easy to understand written out like this. When leaving two or more young female servants to mind the house, you might say "In any case, they're yoman doshi, kakan doshi."

By "Easy to understand," he means that the kanji allow the sentence to be read as something like "equally unable to read, equally unable to write." However, I will confess that his example sentence did not clarify matters for me at all. They can't read or write so they won't pry into personal documents? They can't read or write so they might get in trouble if someone comes calling expecting them to?

Then I thought, I think I've seen this word before. And I had! It's in Hino Sukezumi 日野資純 and Saitō Gishichirō 斎藤義七郎's 1965 Dictionary of the Kanagawan Dialect (神奈川方言辞典): ヨマンドシ (Yoman doshi), with the meaning onaidoshi ("the same age").

This didn't clear things up for me very much. So I looked it up in the venerable 日本国語大辞典. They offer two definitions. The first is literal: "Equally unable to read and write" (文字を読み書きできないもの同士). The citation is an 1801 senryū:

よまんどしかかんどうしの恋も恋
yoman doshi / kakan dōshi no/ koi mo koi
Even between the illiterate, love is love

(This might seem pretty patronizing, and I guess it is really — but of course writing love letters was one of the main ways of performing love back then, especially among the sort of people who would write senryū.)

It's interesting that the dōshi expands and contracts to fit the meter, too.

Their second definition was "Children at around the age where schooling begins. Also, someone who has been in the same [school] grade as another since their youth." (就学前後の幼い子ども仲間。また、幼いときからの同期生。) This looks like a humorous metaphorical application: "equally unable to read and write" because not yet able to hold a writing implement properly, and by extension someone who went through that phase at the same time that you did.

They also offer three dialectical definitions: "Children of the same age" (from Tokyo), "The same age" (from Kanagawa), "Young, immature" (also from Kanagawa).

I wasn't able to find any in-depth treatment of this phrase in particular. But here's what I think happened.

1. First, you have the phrase yoman dōshi, kakan dōshi is coined. It just means "equally unable to read/write." There is variation between dōshi and doshi right from the start, as is very common with words ending in 同士.
2. Some speakers (in Knaagawa, apparently) reanalyze doshi as a voiced form of toshi, "year" or "age" (as seen in words like onaidoshi, "the same age"), giving a word that means "non-reading age, non-writing age," i.e. "young."
3. Meanwhile, possibly influenced by the "young" meaning, other speakers extend the "equally unable to read/write" meaning so that the word can be used to describe people who were unable to read/write (due to youth) at the same time — that is, are the same age, even if they can both read and write now.

So I think that Kaburagi's example sentence is supposed to mean "They're the same [young] age, they'll get along fine." But I'm honestly not entirely sure.