A summary (English and Chinese) and the 理由書 can be found here:
http://jirs.judicial.gov.tw/GNNWS/NNWSS002.asp?id=267570
One recusal, one dissent and one partial dissent. The 理由書 cites opinions of the WHO, the American Psychological Association, the World Psychiatric Association, and, wait for it: the US Supreme Court (Obergefell v. Hodges).
Dissenting opinions were filed by Justice Huang Horng-shya (黃虹霞) and Justice Wu Chen-huan (吳陳鐶).
“Marriage is a union between a man and a woman, who live life together as an institution, which is protected by the Constitution. Making changes would involve altering social and cultural values, which should not be made by merely copying developments in other nations… Therefore, the decision to legalize same-sex marriage should be made by a referendum,” Wu said.
It is a fallacy to rule that Civil Code provisions are unconstitutional, Huang Horng-shya said.
Same-sex marriage is not a fundamental human right to be universally protected, she said.
She said that she supports legislating legal protections of civil unions for same-sex adults, but does not view a homosexual union the same way as a marriage between a man and a woman.
Now for the fallout:
The interpretation represents “the elite of the nation’s judiciary system bullying the majority opinion of the public,” alliance convener Yu Hsin-yi (游信義) said, adding that it is wrong for the “lawmaking body to interfere with justice.”
“We are very disappointed with the ruling and plan to continue to fighting against it with all our might,” Yu told an improptu news conference at the rally site. “We plan to request that the Control Yuan conduct a probe into the grand justices.”
He said the grand justices had “rigged the process” by calling expert witnesses to testify, none of whom stood for traditional family values or the protection of the sacred institution of marriage.
They weren’t satisfied with the government’s representative testifying on behalf of a certain interpretation of Confucianism? Maybe they think he’s not an expert.
And for foreigners:
In response to media queries over whether same-sex foreign nationals could register their marriage in Taiwan, Lu did not give a direct answer, but said they would have to abide by provisions in the Act Governing the Choice of Law in Civil Matters Involving Foreign Elements (涉外民事法律適用法).
From the Global Times article:
"The ruling proves that same-sex marriage is acceptable in Chinese culture, and is likely for the Chinese mainland to legalize gay marriage within a decade," Li Yinhe, a sociologist at the Chinese Academy of Social Sciences, told the Global Times on Wednesday.