That post referenced a British newspaper article whose title was a bit sensationalistic. “Passenger aircraft rivals clash over safety of fuselage built from plastic”.
Airplanes are not built out of plastic, they’re made of carbon fiber. The two are both composite materials, yet interchanging them would be like saying a metal airplane was going to be made out of tin.
The article also states that the Dreamliner will be the first “passenger jet” made entirely of composites, which is untrue. Smaller passenger jets are already made of composites. The Raytheon Premier, for example. The Hawker 4000. The Eclipse 500. The Citation Mustang. The Adam A700. And GA aircraft have been made wholly out of composites from the 1970s (witness the Varieze). Many modern airframes are all-composite (Cirrus, DiamondStar, etc). The 787 may be the first large airliner to be built mostly of composites, but the material and methods have been tried and tested for a long time.
Composites are also insanely strong. I fly aerobatic airplanes that you can put 10 Gs on — an frankly they’ll take twice that without blinking. You stress them that way over and over again. A very hard life for a wing. What’s it made out of? Yeah. Composites. The parts that tend to break are the metal ones (formers, stringers, etc) that you cannot see. Which is Airbus’ whole arguement against composites.
No material is perfect. Everything is a compromise. But I’d have no problem flying (or flying on) a 787.