It'd be interesting to find out how that reputation came about. I've always figured it was due to Sony's explosive popularity in the 80's.
Japan's one of the most nationalist and conservative countries on the planet. Weed culture does not exist, and they give no fucks about homosexuals, let alone trannies. I could see your average American progressive faggot getting major culture shock there.
You're going a bit far the other way there. Barely anyone does weed there, but stimulant drugs like amphetamines are known even among professional types working long hours so there is a substance abuse issue to some extent. They just have different preferences for the illegal drugs the Yakuza sell, and keep quiet about it because Japan allows conviction based on confessions alone.
Also the fact they have some ridiculous gay stereotype in their media shows that they're definitely not one of the most conservative countries on Earth. There's absolutely no way that would be allowed in Nigeria or Uganda where sodomy is illegal, or even on mainland China where depicting homosexuality is banned.