Kimimaro was obsessed with Orochimaru. And there aren't very many well-developed villains in the series. No one would care about the love lives of Akatsuki members who got like 2 fights each.
That doesn't mean he was gay for him. People are obsessed with Jesus, that doesn't mean it's sexual.
and I would care. I think it'd be interesting to see their love life. But they probably don't have any.
Nagato was not interested in Konan
Sasori had a puppet body and never formed relations with anyone
Hidan obviously cared nothing for aside his religion of mass murder
Kakuzu wasn't even human anymore and only cared about money
Orochimaru cares for nothing aside for his experiments. Also he's no longer human
Kisame had fish skin
Excluding Obito, only Deidara and Itachi could have had any sort of possible relationships and even that is iffy.