For starters, Confucian thought is not a religious philosophy at its core, but rather a socio-political one. As such, Confucian works don't really touch on the subject at all. There are vague mentions that some have used to justify an anti-homosexual stance here and there, but these are a stretch in my opinion. Confucius does, however, write extensively about the family unit, and its importance to the state.
Specifically, in Xiao Jing (孝經), literally translated as 'Filial Piety' - one of the core Confucian classics - Confucius highlights the behavior expected of each member of the family unit, from the father, to the older sibling, to one's children, and draws parallels between the family unit to the state. Some anti-homosexual arguments from Chinese scholars quote Confucius in this particular classic. In particular, the argument seems to be that Confucius stressed the duty of sons to procreate ("naturally") and carry on the family line. Counter-arguments on this subject claim this is misinterpreted on purpose, and that Confucian thought bears no ill will or negativity towards homosexuality.
Historically, Confucian thought and its policy (or lack thereof) towards homosexuality has been a nonchalant one. Throughout Ancient Chinese history, homosexuals in Ancient China weren't really persecuted to the same extent of their European counterparts. A Jesuit missionary in Ancient China, Matteo Ricci, in his travel journals (De Christiana expeditione apud Sinas) was quite disapproving of the general acceptance and nonchalance towards homosexuality and prostitution (both male and female). Male prostitutes were not uncommon across various different dynasties.
Even Emperors have famously had male companions who were believed to have acted in the same capacity as concubines. Emperor Ai of the Han Dynasty famously had a male companion (that many scholars suspect he had a homosexual relationship with) named Dong Xian; since the two often slept together on the same bed (in Ancient China, not necessarily an indication of homosexuality over close male friendship; Liu Bei, Guan Yu, and Zhang Fei of the Three Kingdoms period were also noted to have slept on the same bed), one day, the Emperor awoke to find Dong Xian still asleep, his head resting on the Emperor's long robe sleeve; rather than wake Dong Xian, the Emperor gingerly cut off his sleeve. This led to the idiom Duan Xiu Zhi Pi ( 斷袖之癖), or "the cut-sleeve passion", which is used as a romantic literary term to insinuate a homosexual relationship.
Moving onto more recent times, the Supreme Court ruling toward gay marriage in the USA sparked widespread debate in China. This was mainly because Justice Anthony Kennedy quoted Confucius as part of his speech, stating of the ancient Chinese sage "Confucius taught that marriage lies at the foundation of government", a passage from the Li Ji (礼记), or "Rites", a book that has been the cornerstone of Chinese civilization and governance for centuries. The intention of Kennedy nonwithstanding, his words caused furor in China, with people arguing both for and against homosexuality, many trying to use that passage both for and against in a series of different interpretations. This is interesting to observe, as hitherto modern China had handled homosexuality with a policy that can be basically summarized as such: don't approve of it, don't disapprove of it, and don't talk about it.
Now, however, with the issue of homosexuality forced out into the public realm of debate, China will be forced to confront it eventually - like it or not. How exactly they will proceed remains to be seen.