[arnsholt]

I don't have my full array of dictionaries at hand, but the Oxford Latin dictionary (the only one worth considering in my opinion if you want a serious discussion) gives the etymology of scio (the root verb) as possibly related to Sanskrit chyati and Greek schizo (as in schizo-phrenia, actually), both meaning to separate. I can't say for the Germanic connection to shit and friends, but it's not impossible, although I'm not sure where the l comes from.

I'm not entirely sure which root the Sanskrit form should be but it might be chid-, which fits with the Greek. In that case, I'd wager an Indo-European root along the lines of skedH-, with palatal k and laryngeal (IIRC, it's the laryngeal that gives the Greek z).

As for the derivation of the meaning, I think the notion of "separating right from wrong" is reasonable, but these things are often notoriously hard to pin down.

[nemetroid]

My Swedish etymological dictionary (Våra Ord) has this on skita (verb form):

skita: old Swedish, Icelandic skíta; common germanic word (Ger. scheissen, Eng. shit), to an Indo-European root with meaning 'split, separate'