That is, Strangers stand further apart than acquaintances do is ungrammatical? I have often encountered inverted clauses after than, as, so in comparatives, so the sentence above seems - at least to me - to be ungrammatical.
Distance is a reliable indicator of the relationship between two people. Strangers stand further apart than do acquaintances, acquaintances stand further apart than friends, and friends stand further apart than romantic partners.
Social Psychology: Exploring the Dynamics of Human Experience