There is no objection of the Buddha found in the Tipitaka. To be precise, the Buddha was neither supportive nor against marriage between members of the same gender.
This is not because Buddhism is naive about homosexuality. In fact, in the first book of the monastic code, the Vinaya, in the Buddhist Pali canon, there are hundreds of references to sexual relationship and most forms of deviant sexual practices, as appeared in Indian society over 2,500 years ago.