The phrase I'm wondering about is "causas sui odii" — 'the cause of their hatred'. The men are discussing the cause of their (the men's) hatred? or the cause of their (the women's) hatred? If it was the women's hatred would it be "causas suae odii" or could this phrase be translated either way depending on the context of the whole paragraph? Thanks in advance for your help.
The form of suus (and meus and others) only depends on the noun it modifies. The gender, number, or other details of the owner do not matter at all.
It might be helpful to think of suus as an adjective. In particular, one should not consider it as a form of se/sibi, but as a related adjective. Then the right form comes more automatically. This adjective just happens to mean "possessed by them". Indeed, these pronouns are sometimes called possessive adjectives.
Therefore it would be sui odii because of the form and gender of odii. The genders of the human parties involved are irrelevant.