It seems the Purifier Protoss can only gain access to the Telepathy discipline if they take the class Fateweaver (Khaydarin Acolyte). It seems strange that they get the discipine focus talent for telepathy with Solarite Magus (Psychic Master)... but cannot access it without the other class.
Is there another way to unlock the discipline that I am missing?
It is correct, all psychic masters, no matter which protoss sub-race, gain telepathy discipline focus through Psychic Master. Purifiers, however, do not have telepathy by base, so they gain no benefit from this unless they also take fateweaver. This is just because the base class benefits are static no matter which tribe takes it, and that was a universal benefit to taking the psychic master. For purifiers, that level will be a little underwhelming. But purifiers have a lot going for them already.
Protoss are also meant to level multiple classes over their career so its probably intended that if you want the focus you do both classes
There is not, at least not that I found. Seems the Fateweaver variant for the Purifiers was made specifically to let them do that. Makes sense too, small price to pay to be able to play a mechanical Protoss.