Disclaimer that I'm not a linguist and I'm just someone who has read too many wiktionary entries
Words marked with * are reconstructed
There's linguistic evidence that red dye at some point/in some places was made from worms. Specifically Kermes vermilio, which are technically scale insects, turns out.
English "vermillion" <- Latin "vermiculus", little worm - from "vermis", worm in Latin.
English "crimson" <- Persian کرمست (kermest), "carmine" is also related. From the same Proto-Indo-European root! Did you know that Persian is an Indo-European language? I'm not ashamed to admit that I didn't.
These two words are theorized to be connected to Sanskrit कृमिज (kṛmija).
Proto-Slavic *čьrvenъ is formed from *čьrvь - worm, and;
From that we get Ukrainian "червоний" (červonij), Polish "czerwony", Russian "червонный" (červonnyj) which is now replaced by "красный" (krasnyj) and that's a whole other story, which I feel obligated to tell.
In Proto-Slavic there was a word *krasa - "beauty". From that word was formed *krasъka - "paint", literally meaning something close to "beautifier".
Verb form *krasiti meant "to beautify", "to decorate". In Russian this meaning was influenced by "paint" (my assumption) and now modern Russian "красить" means "to paint".
Now, something more drastic happened to the adjective - *krasьnъ, formerly "beautiful" and at this stage "painted". Somehow - maybe, the most obvious paint to everyone was red paint, or some other reason - it started to mean "red", and it only happened in Russian. And as I mentioned, in one of its closest relatives, Ukrainian, the worm-based word "червоний" is still used.
Curiously, this "beautiful" -> "painted" -> "red" shift didn't affect all occurrences of the root. For example the word "прекрасный" (prekrasnyj) still means "very beautiful", and "краса" (krasa), however archaic, is still recognized as "beauty".
