To a point, yes. I know trans and gay couples and it's complicated. Gender marker changes still require bottom surgery and ability to marry requires opposing genders on their koseki.

The conservatives don't want to change the koseki system (which foreigners can't even have and is another problem). The conservatives don't allow couples to have separate names (unless one is a foreigner and thus no koseki name shenanigans). It also plays into the "(the right type of) people aren't having enough babies!" thing. I do know one couple who are both trans but did not have surgery wnd did have a kid which is the type of situation the government largely doesn't care about

Edit: ah, I live in Japan for context (married to japanese, but not a japanese national myself). Here over a decade noe