How can the hadiths that affirm that a believer may commit adultery or theft be reconciled with the hadiths that deny the attribute of faith to the perpetrator of these major sins at the time of their commission?

There is no contradiction between the texts of Sharia. Any apparent contradiction is due to the invalidity of a statement attributed to Sharia, or a misunderstanding. The first hadith, which includes "Does a believer lie? He said: 'No,' then followed it with: ﴿It is only those who disbelieve who invent falsehood﴾ [An-Nahl: 105]," is a fabricated hadith because of Ya'la bin Al-Ashdaq, who is accused of fabricating hadith. As for the other hadith, which negates faith from the fornicator, the thief, and the wine-drinker, it is authentic and agreed upon. Its meaning is that the perpetrator of major sins exits from the complete, obligatory faith, but not from the root of faith. This is the doctrine of Ahlus-Sunnah wal-Jama'ah, contrary to the Khawarij and the Murji'ah.