I am in a same sex marriage now, but I was also was an international student with a relatively weak passport (Indian citizen, though I was a student in the US). While I was a US student, I got tourist visas within the US to the UK and EU with no issues, they just wanted to confirm that I was enrolled. One trip was to visit family in the US, the other was to visit a friend who was also an international student in Germany. Obviously there is always the risk of being rejected, but it was a very smooth and easy process.
After finishing my US undergrad I also got a B1/B2 for the US (albeit from India) with no issues, though of course I did not have a boyfriend at the time, we met when I came back for grad school a couple of years later.
It can be a little scary but you are in a developed country already and presumably following the regulations in Japan that relate to a student visa. I'd apply, worst thing that happens is you get denied and go meet up in Thailand or something instead.