"Sounds like the Parsis absorbed the Hindu idea of caste from their new neighbors."
Caste??!! There you go again!
Tell me what exactly in the article made it sound like that? Whats has "caste" got to do with Parsis not allowing converts into their folds? Could you explain?
Refusal to intermarry or allow converts, to an unreconstructed Eurocentrist like myself, looks remarkably similar to the Hindu caste system, with the Parsis as a group forming the functional equivalent of a "caste" within the general Indian system. As far as I know, the Parsis are not into reincarnation, thus eliminating the ideological basis for true caste.
As mentioned, ancient Zoroastrianism was highly evangelistic, often launching persecutions of other religions. The refusal to accept converts is new, presumably since their flight to India.
Other religions have of course gone through similar phases, notably Judaism, which went through various attitudes towards converts, varying from forced conversion under the Maccabees to the marked reluctance to allow conversion shown by many of today's Orthodox groups.