I understand Japan is conservative when it comes to LGBTQ issues
Your understanding is very wrong. Japan was long ahead of most Western countries in many ways, especially transgender rights. The only thing really lacking now is marriage equality, but it's more "when" than "if" - the public is in favour of it, but democracy is a slow-moving system designed to preserve the status quo, so legal change takes time.
Notably, Japan is not a Christian country. While there are many people that are indifferent to LGBTQ rights, the percentage of the population that rabidly hates gay people is significantly smaller than countries where ~half the population define their lives around a 2000 year old book that tells them to stone the gays.