It's old people. Old people will eventually die and then young people who are either activists or simply like me and aren't super pro-gay rights but have a hard time coming to grips with why people should be legally discriminated against will run things. Most places not ran by regimes aiming to strictly control the thoughts and opinions of citizens and aren't lynching people for being gay are going this route, if for no reason than gay people are coming out of the closest, not seeing why they should even have to be in the closet, and are being more public than ever so you're going to have to deal with them and their issues whether you like it or not. Even for places not like that, if you have the internet you get exposed to how it is other places and it broadens your views on what's possible and things slowly start to change from there.
Anyways, Japan doesn't seem too homophobic or at least not radically more so than the US. We don't have major video game and comic genres dedicated to men and school boys having sex with each so that in and of itself has to be a sign of some level of acceptance.
Hard for me to say. I'm from a southeast Asian country that doesn't think highly of homosexuality. Being a 1.5 generation, I still hold their old ways while adjusting to American ways. I'm on the fence on homosexuality. I'm hypocritical. I don't support it, but I don't go against people's choices of whom they marry, race or gender, etc. For this topic, it depends on folks. I wouldn't say Japan is homophobic. You can't say America is homophobic when only a few states have legalized gay marriages. The conservative folks, the older ones, are against it. It's considered a deviancy against norms of marriage in many societies. Compared to America, homosexuality is more open than Japan. Also, there is a biological aspect. How do humans survive since we cannot breed with 2 same genders by natural means?
With the way you phrased it, wouldn't that point to the opposite in that America is homophobic; that you can say that America is homophobic because only a few states have legalized gay marriages?