Kosmonaut seems to be spot on: semantics are absolutely necessary for tracing back personal pronouns to their antecedents. Sentences 1 and 2 are perfectly acceptable in formal and informal English, both old and new. The same applies to most other Indo-European languages. But it is important to distinguish between the different kinds of pronouns; relative pronouns, for example, have an unmistakable syntactic link to their respective antecedents.
A. I gave some bananas to the women, who were rather hungry.
This is standard.
B. ?I gave some bananas to the women, which were larger than expected.
Somewhat bumpy, but I'd say still acceptable, because the distance between pronoun and antecedent is short, and because the pronoun "which" is restricted to inanimate objects.
C. I gave the bananas to the monkeys that were there.
Somewhat ambiguous, but, lacking strong semantic clues, the reader will not have much doubt that "that" refers to the monkeys. In speech, the use of accents could make the pronoun a bit more flexible.
D. *I gave the bananas quickly, before the storm reached the forest, to the friendly but fastidious monkeys that I had kept stored in the freezer.
Impossible, because the distance between bananas and "that" is far too great.