You clearly missed the convenent, a rather bloody scene, involving torn animal bodies and genital mutilation.
He even took a new name, which is what you do when you convert.
That said, the point being Jews-by-Choice must be treated the same as Jews-born-of-a-Jewish-Mother is expressly stated about twenty times in the Torah.
In fact, one may not remind them that they converted, as that is a violation of the Law.
Some of the best Rabbis, ever, were converts.
Period.
Then we have that fellow David, whose great-grandmother was not an Israelite but who through faithfulness to her late husband followed her mother-in-law back to Judah and married another Jew.