At redaction time of this message at least three aicraft manufacturers do build plastic planes, namely:
Diamond aircraft which build single engine (DV20 Katana and DA40 Diamond Star) and twin engine piston DA42. The high performance single DA50, which made its maiden flight in early april.
Cirrus design offers various variants of its high performance single engine SR20 / 22, including turbo versions. One specific feature is its side stick, looking really airbus like.
Columbia also builds a high performance single engine, the Columbia 400.
Obviously, the new Airbus and Boeing planes, not to mention Embraer, are mostly fitting the plastic airframe criteria, but unfortunately, I did not found any club operating such planes until now. If you know one... please let me know.