Final answer:
Paul McCartney and Ringo Starr quit during the recording of the White Album due to tensions within the band and disagreements over the musical direction of the album.
Step-by-step explanation:
The two people who quit during the recording of the White Album were Paul McCartney and Ringo Starr.
Paul McCartney left the recording sessions temporarily due to tensions within the band and disagreements over the musical direction of the album. He later returned and continued to contribute to the album.
Ringo Starr also briefly left the recording sessions due to similar reasons. He felt excluded and undermined within the band, leading to his decision to quit temporarily. However, he later rejoined the sessions as well.