This is an excellent question! I had to do some digging as I frankly had never considered this scenario...and neither had the nazis when they wrote the Nuremberg racial laws! As you might suspect, the Nuremberg laws were all about blood. A Jew was defined as anyone with three Jewish grandparents; or with two if they met some other conditions which you can read about in this translation (pdf). It doesn't mention converts to Judaism of what they would have called “pure German blood”, i.e. non-Jewish ancestry, at all, probably because they couldn't imagine a “pure” German would do such a thing. To be fair, it was very rare at the time.

They did run into some cases, though, and then it was up to the courts to decide what to do. Two such cases are cited in Raul Hilberg's The Destruction of the European Jews (volume one, p.77-78) and in both cases the court decided that the individual was to be considered Jewish for as long as they themselves considered themselves Jewish, or as the first court put it “in cases when the individual involved feels bound to Jewry in spite of his Aryan blood, and shows this fact externally, his attitude is decisive” and the second: “[an individual] who is racially a non-Jew but who openly claims membership in the Jewish community, belongs to the community and therefore has placed himself in the ranks of the Jews." This seems to imply that they could save themselves by renouncing their Jewish faith. These cases both involved men who had married Jewish women and they were heard in 1942 and 1943 respectively, at a time when it was abundantly clear that to declare yourself Jewish was life-threatening, so let's spare a moment to honour the memory of these heroic individuals.

Hilberg also mentions a well-known nobleman, Baron Ernst von Manstein, who converted and later married a woman who had also converted. They both refused to renounce their faith. His connections prevented them from being deported and they both died essentially of old age during the war. Source