No, gay marriage is what the US culture war pivoted on for a long time because it doesn't involve disruption to normal cishet social currents and doesn't require anything of the state actually be provided to people, plus it represents a benefit to the gay members of the bourgeoisie just as much as to the common person.

Furthermore, like in Taiwan, gay marriage in the US was not approved by referendum, it was basically a fluke from the Supreme court independent of other efforts. There are still nearly as many states as before where it is a large popular sentiment that if your kid is gay, they are sick, and state legislatures that are, as we speak, preparing to bring gay marriage back to the SC to get its protection removed.

Edit: As an aside, despite your chauvinistic, idealist view of cultures being "there yet" or not, using China as the example, lateral cultural differences also exist, and ignorance of these makes it very difficult to actively evaluate what a cultural attitude is. In China's case, there is in most places a passive homophobia (which is still homophobia), but they generally don't have the same homophobic culture war front that we saw in America. They are more like a broad, cultural "don't ask, don't tell", which is in keeping with even Imperial Chinese traditions. There is obviously resistance to the existing movements to do things like legalizing gay marriage, but it's a losing battle for the conservatives, who are mostly passive on this issue, and several of the practical benefits of gay marriage have already been won by other concessions, allowing gay couples rights concerning medical and financial decisions and so on through their guardianship system.

All this to say "Is gay marriage legal?" should not be treated as a binary for queer people having any recognition.

P.P.S. China also has multiple dedicated clinics for transgender people in various cities like Beijing and Shanghai.