"I find it hard to appreciate his opinions."
Translation:Jag har svårt att uppskatta hans åsikter.
No, sina is used as a reflexive possessive adjective that refers back to something earlier in the sentence. Sina would be used to mean "his/her" when "he/she" is mentioned earlier in the sentence. For example, Han älskar sin fru (He loves his wife). If you said, Han älskar hans fru, that would mean that he loves someone else's wife. It would not even be grammatically correct in the sentence you asked your question about (it could be grammatically correct but nonsensical in other sentences).