Please note that as far as the Germans were aware only five Jews arrived at Auschwitz on KHM's RSHA transport. 1x male (No. 112272) and 4x females (Nos. 39837-39839 and 39852).
It seems very likely this is the case. In her book "Return to Auschwitz", KHM tells that when arriving in Germany after escaping the Ghetto she assumed a false Polish identity - Leokadia Dobrzynska (page 57) - but when captured by the Gestapo her Jewish identity and her real name - Kitty Felix - were revealed (page 69). However, later in the story it becomes unclear whether she was deported (reportedly from a prison in Dresden), as a Jew or as a political prisoner. According to KHM, her transport included Russian women and German gypsies among others. So it was definitely not a pure Jewish transport. I looked up some names of prisoners in her presumed transport (arriving April 2, 1943) in the list provided by AB Museum Archive - e.g., Maria Mlodzik (39845), Maria Matlak (39847), Maria Orlicka (38949), Franciszka Remosz (39853), Stanislawa Krolikowska (39855) - definitely not Jewish names.I suggest KHM like Zywulska kept her Jewish identity secret and was held in Auschwitz as an ordinary Polish political prisoner.
It is indeed strange that her book does not address clearly her Jewish or false Polish identity in Auschwitz. Yet, in one place in her book she portrays herself as a political prisoner. This is when she tells about being spotted by the SS man Bedarf writing a letter - a forbidden act. Her Kapo gets her off the hook by telling the SS man that she is a political prisoner writing to her mother, who is also a political prisoner (p. 159).
I once read a testimony by a women imprisoned in Pawiak as a Jew and then deported to Majdanek with a group of Polish political prisoners. She was lucky to be admitted there as Pole. So KHM and her mother may be similar cases.