Nobody expects the Spanish Inquisition, especially on Gethen, where they never had one. But they do have religion, and a bit of turmoil to go with it. The Left Hand of Darkness's two religions, Handdara and Yomeshta, have some major differences about the proper use of knowledge. Handdara promotes wholeness from opposites, seeing both light and shadow as necessary and useful. Yomeshta, on the other hand, sees one path as worthy (the light one) and the other as unworthy (shadow). These differences might not be much to fuss over, except when religions get used toward political ends. Now that could be a problem.
Le Guin is less concerned with an individual's relationship to religion than with religion's role in society.
Le Guin used Taoism as the basis for Handdara, because it can serve as both philosophy and religion.