All I know is that a "Parsee" - which according to the Grove Dictionary is what Sorabji père was - is one of the descendants of those Persians who fled to India in the seventh and eighth centuries to escape Muslim persecution, and who still retain their religion (Zoroastrianism); in other words a "Guebre."
The term parsee/parsi was originally one with which Zoroastrian adherents were dubbed by locals when they arrived in India. It may have originally indicated Persian ethnicity, but might also just be a more general term to indicate people who had probably come from Persia? (The Zoroastrian belief in Persia attracted many adherents from all parts of Middle Asia, and accepted them all willingly - Persian or not). The term was only adopted by the Zoroastrian community in India much later, but they now use it enthusiastically. There appear to have been two distinct waves of migration of Zoroastrians from Caspian parts to India. The first was in the C10th, when the community in Persia suffered greatly from religious persecution there. The second came in the latter C19th, when the community at the Surukhany Fire-Temple (in what is now Azerbaijan, and was then the Kingdom of Persia) became convinced of the need to relocate. This is generally attributed to the weakening of the natural gas jets which percolated directly out of the ground at the Temple, and caused the appearance of fire springing from the very ground, witnessed by Polo and other travellers. (Of course, Azerbaijan remains a major producer of gas and petroleum products today, even if the particular field at Surukhany has dropped to a trickle). The rise of Bolshevism in Persia put the final lid on Zoroastrianism as a major force, but even in 1983 when I visited Surukhany there were still a few wizened wisebeards tending the temple. "Sky burial" (ie leaving the corpses of dead adherents on rocky outcrops, so the vultures took the bones) was forbidden by the Soviet authorities - a major tenet for Zoroastrians, as I was led to believe by one of the old men I met there.
The present authorities in Azerbaijan - the Aliev Dynasty of allegedly "elected" "democratic" leaders - have no greater love of religions which might usurp their autocratic authority, and whilst they are pleased to have the tourism revenue from gawpers at Surukhany, they certainly want no return of a belief (or believers) which might not cede precedence in all matters to the Aliev family.
Perhaps Mr Hinton can tell us more authoratitively about Sorabji's personal background and beliefs? Clearly he must have had strong convictions that led him to change his given name?