“I differentiate between the Yidden and the Goyim who think they’re Jewish.”
That is indeed very important. As the Lubavitcher Rebbe says, when a goy is told by a “rabbi” that he is a Yid, not only does it bring a terrible churban for the Jewish people, but also for the goy himself (e.g., a goy who keeps Shabbos is חייב מיתה).
Last week, I met someone on the street who excitedly told me that he is Jewish and he wants to learn more about his heritage.
Before putting on Tefillin with him, I asked him to clarify his roots. It came out he was genetically %59 “Jewish” from his father’s side.
I politely explained him that Judaism does not consider him Jewish, and that he must serve G-d as a righteous gentile (sheva mitzvos).
He walked away quite dejected, but much safer than if he wouldn’t have known, חס ושלום.
Boruch Hashem, it is usually easy to be מברר if someone is halachically Jewish or not (aside from when it comes to marriage when we are more מחמיר to be %100 sure).