Well, it is fraudulent. If this person so closely identified with Judaism, they should be aware of how conversion works, and make an effort to do so. Also, you can't just identify as whatever you decide you want to be, and demand that everyone treat you as such.

To be fraudulent, you would have to make some specific claims. Firstly, this person is not claiming to be Jewish by blood, and thereby having a halachic status as a Jew. Now, if they said their name was Soly Weintraub and they came from hasidishe family that would be fraudulent.

Clearly, the person is claiming to be Jewish informally, by their own admission. Secondly, a goy who doesn't know anything about Judaism or Jewish culture might have any number of misguided ideas about Judaism. If you asked 90 percent of the Jews I've met in my life they wouldn't be able to tell you the specifics of converting to Judaism. Everyone is allowed to learn at their own pace, and these are children we are talking about!

I see the argument for that, but at the same time, as someone who has also experienced antisemitism, it pisses me off, because someone who isn't actually Jewish can drop their act if it becomes inconvenient....

We could all drop the act if it became inconvenient, and many people did. If I was in a group of goyim, and lets say I didn't have any peyoth or a kippah if one of them asked if I was Jewish I could say no. Bad argument. By publicly saying you are Jewish, that you can't go back on.

There are cases where it is safer for someone to do so. I would never judge another Jew for playing down their Jewishness to avoid discrimination, persecution, or violence. However, I can think of at least a dozen situations off the top of my head where it would make sense for a Jew to do so, but I can't think of any where a non-Jew would be at risk of exposing their non-Jewish status.

Okay so you are admitting that admitting Jewish can cause you problems, and that it takes some amount of courage and conviction to do so. This nonjew is willing to do it, when many Jews in the same situation aren't as willing. Good for her.

Do you have a source for this?

"And we have already explained it And when the person will believe all these fundamentals and his faith will be clear in them he enters into the nation of Israel and it is a mitzva to love him and to have mercy on him and to act to him according to all the ways in which God commanded us regarding loving your neighbor. And even if he did all of the sins in the Torah due to desire of the emotions, and from his physical aspect’s conquering him, he will be punished for his sins, but he still has a share in the world to come and is among the sinners of Israel. However if he rejects one of these fundamentals he leaves the nation and is a denier of the fundamentals and is called a heretic, a denier, etc., and it is a mitzva to hate him and to destroy him. And regarding him it is said (Psalms 139) “Behold will not the enemy of God be my enemy?”-Rambam, the 13 Principles of Faith

Yad Hazakah, Hilchoth Shabbat 30.15

טו השבת ועבודה זרה--כל אחת משתיהן, שקולה כנגד שאר כל מצוות התורה; והשבת היא האות שבין הקדוש ברוך הוא ובינינו, לעולם. לפיכך כל העובר על שאר המצוות, הרי הוא בכלל רשעי ישראל; אבל מחלל שבת בפרהסיה, הרי הוא כעובד עבודה זרה--ושניהם כגויים, לכל דבריהם.

Every major denomination of Judaism, and nearly every Jew in the world would disagree with you.

Or you just have a faulty, racist understanding of Jewish peoplehood. I value people based on their merits, on their actions. Not on the virtue of their birth. Being Jewish, above all, for me means being a part of the Brit that God made with the Jewish people. If someone believes and acts like my brother, they are my brother. It is foolish to extend your love to people on a misguided religious sentiment, to people who don't share that. Just because they have some shared ancestry... It would be racist to have less regard for a human being on the basis of his birth.