In 1992, a gay US Marine stationed in Japan was murdered. Soon after the murder, an SDF leader was interviewed by a weekly magazine and was asked about gays in the Japanese military. I have never heard about it. Though the SDF is a volunteer organization, and is always lacking recruits, openly gays and lesbians who try to enter the SDF will not be accepted. If some soldiers do come out publicly, they would probably be punished.
Japan is one of the most intolerant countries with respect to accepting refugees and immigrants.
There are other very strict terms one must meet in order to qualify for refugee status. Even if one has satisfied all the requirements for refugee status, the Japanese Government has discretionary authority to reject the application. The Japanese government recognized only 1 case as suitable for status as a refugee. We have to change such an intolerant policy, but it is very difficult. Given the reality I have outlined above, I am afraid the Japanese government doesn't have the tolerance to accept gays and lesbians as refugees.