However, the Buddha has warned very clearly that lusting in a sexual sense is one of the causes of suffering (Saññoga Sutta, AN 7.48: https://www.accesstoinsight.org/tipitak ... .than.html).
While it is true, that only male and female are mentioned in the Saññoga Sutta, reading through the Parajika offences in the Vinaya it is made clear, that the term 'sexual intercourse' is not to be understood to be restricted to human male-female couples (as one Bikkhu found out, as he tried to weasel out of this restriction by having sex with a monkey).
Instead, the term 'sexual intercourse' in a Theravada sense refers to all kinds of intercourse involving genitals (literally, the “urine path” (passava-magga) —i.e., a woman’s vagina or a man’s penis); the anus (vacca-magga); or the mouth (mukha) and encompasses any voluntary intercourse with a human being, a “non-human” being (a yakkha, naga, or peta), or a common animal, even with body parts. It matters not if they are female, male, neuter, or hermaphrodite.
https://www.accesstoinsight.org/lib/aut ... o/bmc1.pdf
A very wide field -- nobody should say that people in historic times were not very inventive, so the Buddha made sure that absolutely everything was covered unmistakably! -- so any gay relationship would also be well covered.
To conclude, there is no arbitrary rejection of homosexuality in Theravada.