The Left Hand of Darkness presents a lot of ideological issues as it explores the clash of two vastly different cultures. Regarding the sexuality of the Gethenians, the most significant challenge seems to be acceptance of something completely foreign.
There is a term used in theoretical approach to science fiction: the novum. It means something we encounter in sci-fi that has no equal or comparison in the real world. It is usually strange, a little weird and it takes time to find the words to even describe it—sometimes for both characters and readers. In Le Guin's novel, the novum of the ambisexuality hits the protagonist Genly Ai hard. He struggles to come to terms with the concept and the culture that has formed around it. His own experience has been built on completely different building blocks and while he theoretically understands how the Gethen society could work without a fixed sex/gender, he can't seem to grasp the practical part of it. Genly Ai's own mind keeps wanting to force the Gethenians into the box he thinks in. For him, it's initially impossible to imagine or interact with a culture that doesn't give him the social cues he's used to.
The ideological challenge in the novel is whether Ai can accept the novum or will it present too big of an obstacle. As the story progresses, he learns that by letting go of preconceived notions of human interaction, he can achieve meaningful communication.