Milhouse,
“However, what makes you think there are a significant number of such people? How exactly would “female non-Jews erroneously got mistaken for Jews”?”
Of course there aren’t a significant number. But over 2,000+ years there are going to be some. Another example might be a Jewish family adopted and never properly converted yet she thought she’s Jewish. Or a Jewish baby switched at birth with a gentile baby. (One such scenario was discovered 100 years later, recently.) And had children and grandchildren etc. all thinking they’re Jewish and intermarrying real Jews.
What will happen to these Shomer Torah uMitzvos pseudo-Jews when Moshiach comes and all those generations now realize they’re goyim (who might have had children with actual Jews)?