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Just to clear my mind from that idea, some vague and ill-formed thoughts about personhood in the UFP.
Warning: I'm not very knowledgeable about Federation laws and such - I'm just riffing on my superficial memories of the series, so this could be all wrong.
It makes little sense for a multi-species society like the Federation to have difficulties granting personhood to artificial intelligences. Given the heterogeneous nature of the entities they encounter, a default presumption of personhood must be, at the very least, a reasonable diplomatic stance.
Holodeck technology, in particular, poses worrisome questions; clearly the Federation draws the line between simulation and entity quite beyond the one implicit by the Turing test. As the Federation has granted at least implicit personhood to all sorts of non-organic beings (the classic "living energy pattern"), the decisive test cannot be one of substrate.
But if, say, an EMH isn't denied default personhood on account of his non-organicity, and clearly passes all sorts of variations of the Turing test, the only remaining criteria is that of genealogy: the Doctor isn't considered a person by the Federation legal system not because any particular characteristic he might have or lack, but because he was made.
It's a possible societal reaction to holodeck technology, yes (makes it easy to deal with all sorts of ethical and political problems), but it's a hell of a problematic one, morally.