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The phrase originated in the community Order of the Blessed Saint Scully the Enigmatic, a group that modeled itself and used joking references to Roman Catholic religious orders.
In 2001, a fan wrote an essay about her plastic incarnation and how it changed her life. See: How a bit of plastic can unite the world.
Use in Early Fanworks
One use of plastic incarnations was in late-90s original audiovisual materials where fans re-enacted or reworked X-Files scenes by matching existing audio tracks with visuals of officially-licensed Barbie dolls ("plastic incarnations" of the main characters). These short video segments were produced by a fan named BDodd, who also produced video materials for the cons she attended. BDodd appears to have been a professional or had access to professional video-editing equipment. In a period where vidding -- especially digital vidding -- was cumbersome, rare, and somewhat secretive, these vids, referred to as PIs, were reasonably well-known and circulated within the fandom, and a number were included on convention souvenir videotapes, e.g. those of the OBSSE 1999 gathering.
From July 1999: "It's here! The annual OBSSE Fest Extravaganza newsletter made possible by all those wonderful Sisters and Brothers who attended this year's festivities in the thin air of Winter Park Colorado at the Beaver Village Resort. This year's FEST was a delightful gathering of 75 of the Abbey's finest and the events that took place are detailed for your enjoyment in typical irreverent OBSSE fashion. We had everything: prancing, lard, Not!videos, Scullyritas, cheese, Plastic Incarnations, games, public embarrassments, and more laughter and fun than would be possible to adequately describe. 
For more about "Plastic Incarnations," see "MauiGenesis: A Plastic Incarnation Travelogue" - produced and directed by Sister Autumn; script by Sister Paula