What physical mechanism produces the quasar redshift dipole?

That would be the gravitational pull from the quasar on the light it emits, just as it is for galaxies. Quasars are giant balls of fire producing an enormous amount of energy, which implies they have as much mass as a galaxy, or more. In fact, according to Dr. Halton Arp, quasars are born from galaxies; he showed this by detecting the filaments connecting galaxies to quasars. So a quasar is going to have as much mass as a galaxy, and if the redshift dipole from galaxies is caused by the gravity of the galaxies, it will be the same for the quasars.