Is it permissible for a third-gender individual or someone with low sexual desire to lead congregational prayers?

As for someone with low libido, like an impotent person, his imamate is valid. However, the imamate of an intersex person (khuntha mushkil) is not valid for men nor for other intersex individuals, due to the possibility that they might be female. Their imamate for women is valid according to the majority of scholars.

As for someone who imitates women, his imamate is subject to detailed discussion. If it is due to his natural creation, he is not blameworthy, his imamate is valid, and he is enjoined to strive to abandon it. If it is an intentional imitation and affectation, then he is sinful and a transgressor (fasiq). His imamate is disliked by the Hanafis and Shafi'is, and this is one narration from the Malikis. The Hanbalis and Malikis, in another narration, stated that the imamate of a transgressor is invalid.