Japan does not grant citizenship to those born here. There are multiple ways to acquire Japanese citizenship, most of which are based on the most recent couple generations of parents/grandparents. Multiple citizenship technically isn’t allowed, either. Anyone naturalizing to Japanese citizenship must relinquish their existing citizenship(s) unless the other country does not allow relinquishing. If found out, the Japanese government can take action to revoke citizenship (or at least parts of it; there are actually court cases about this).
In Japan, you can be on the hook (sued) for knowingly engaging in a relationship with someone you know to be married. It’s usually about breaking up the marriage, from what I understand. Sex of the people involved doesn’t matter here.