Do you mean groups of historical converts, or contemporary individuals who converted via marriage etc?

As far as historical converts, the Karaites were a group of Crimean Khazars whose Jewish origins are still disputed. They have a Mosaic religion due to their elite having converted to Judaism sometime in the 8th century. In 1934, German Karaites petitioned the Nazi government to be exempted from racial purity laws, citing a 1791 ukase of Catherine the Great which had declared them Russians, who had later converted to Judaism. The Reich Family Purity Office declared:

The Karaite sect should not be considered a Jewish religious community within the meaning of paragraph 2, point 2 of the First Regulation to the Reich Citizenship Law. However, it cannot be established that Karaites in their entirety are of blood-related stock, for the racial categorization of an individual cannot be determined without … his personal ancestry and racial biological characteristics...

As such, they were exempted from the Nuremberg Laws. On the eastern front, some Karaites were murdered in Einsatzgruppen actions during the opening periods of Operation Barbarossa, but eventually were exempted and left alone.

Another group whose Jewish roots were debated by the Nazis were the Mountain Jews of the Caucasus. As the Wehrmacht occupied the area in 1942, the status of the Mountain Jews became a matter of serious debate between the regular army and the SS. Several massacres of hundreds of Mountain Jews by the SS resulted in protests from the Wehrmacht, which hoped to maintain good relationships (collaboration) with other native groups in the area. Some groups of Mountain Jews were able to convince the SS that they were Tats, and as such non-Semitic people.