Japan does technically allow Muslims in, however their lives are monitored rather heavily and it very, very hard to rent a living space, to say nothing of buying a home.
Also, the steady apprehension of everyday Japanese people to any person in mideast garb and/or long beard is extremely reliable —those images are VERY tightly associated with terrorism, violence and anger, much more so than in the USA.
Even a native Japanese woman with a good background but who marries a Muslim foreigner and decides to go around in Arab garb is regarded as a scary freak —One To Be Avoided.
I have seen it —the woman becomes a total foreigner in her own country.
Japan will NEVAR face take-over by Muslims, though they face many other dangers.
What other dangers do they have to worry about? My daughter wants to go there.