I refer to the legal recognition of the 3rd gender in India, and by extension, a kind of 3rd sex (though I actually refer to gender, where sex is related to the the definition of the gender). It is easy to find this information online. Many Kinnars are not castrated and many of them are partially female. Religious conservatism in India has developed only in recent decades, since the 1990s. I've not heard anything about castrating gay men.

Most cultures use a gender binary, having two genders (boys/men and girls/women).[3][4][5] In cultures with a third or fourth gender, these genders may represent very different things. To Native Hawaiians and Tahitians, Māhū is an intermediate state between man and woman, or a "person of indeterminate gender".[6][better source needed] Some traditional Diné Native Americans of the Southwestern US acknowledge a spectrum of four genders: feminine woman, masculine woman, feminine man, and masculine man.[7] The term "third gender" has also been used to describe the hijras of India[8] who have gained legal identity, fa'afafine of Polynesia, and sworn virgins.[9] A culture recognizing a third gender does not in itself mean that they were valued by that culture, and often is the result of explicit devaluation of women in that culture.[10]

https://en.wikipedia.org/wiki/Third_gender

The word "hijra" is a Hindustani word.[12][13] It has traditionally been translated into English as "eunuch" or "hermaphrodite", where "the irregularity of the male genitalia is central to the definition".[14] However, in general hijras have been assigned male at birth, with only a few having been born with intersex variations.[15] Some Hijras undergo an initiation rite into the hijra community called nirvaan, which involves the removal of the penis, scrotum and testicles.[11]

https://en.wikipedia.org/wiki/Hijra_(South_Asia)