I can't comment on the "Authenticity" but based on my research: Out of the 150+ mosques located in Japan more than 60% of them don't get enough guests or foot traffic to keep the "lights on" (they suffer low attendance and financial problems) not to mention bringing down the amount of foot traffic in the surrounding neighborhood, even in major places like Shibuya. It's a similar situation with church's in Japan as well. A friend was asking me why this was the case and I told him it's simple. "If you're a tourist or even a person in Japan. Would you rather walk into a Buddhist temple, a shinto shrine, or a Mosque?" It clicked very quickly for him. Japan doesn't need more mosques, the mosques that are there are already struggling.